How does the mod handle productivity modules?
EG: Forging 14 gears from 20 iron, and then melting it back down for more iron than you started with.

How does the mod handle productivity modules?

It is would forbid placing the productivity modules into the machines, but it's not implemented yet. Edit: fixed now
You can check if this scheme worth building.

The difference is you get recyclate, instead of iron plates. Recyclate needs to be smelted in order to be useful. It's kinda getting extra ore.

Ok done a little bit of testing and I'm afraid your mod has a big problem with those production modules in the fact that with relatively simplistic production chains. In short via using the modules you can make infinite resources (Iron, Copper, Steel & Plastic) as long as you've got power.

Every time a product passes through a moduled furnace (Production lvl 3) It'll gain 20% extra value and every time it passes through a moduled Assembler Mk 3 it'll gain 40% extra value. This is generally fine in a vanilla setup since it's a one way process, but with your mod you can basically roll back to the start of the chain with the accumulated value still intact.

As an example 100 Iron plates are converted into iron sticks in a moduled assembler 3 this will spit out 140 (40% extra) worth of iron sticks (280), your shredder will then convert those back into 140 Iron Recylate which will then go into a moduled furnace to spit out 168 (20%) Iron plates, which you can then send back to be made into 235.2 worth of iron sticks again.This tallies up to 168% output per cycle.

As such 100->168->235.2->282.2->474.2->796.6->1338.3->2248.3->3777.2 and so on continuing to exponentially increase as long as you have the infrastructure to support continued growth.

If you're ok with this state of affairs not a problem there after after all mods that allow the production of infinite resources with vary degrees of complexity.

If you are not however I don't think there's an elegant or easy solution. Even if you disallow recylate to gain extra production (in smelting) the moment an item's been turned back into a plate/bar an intermediate product or a product that can be used in an intermediate product it's going to start "creating" more of itself relatively speaking.

As such 100->168->235.2->282.2->474.2->796.6->1338.3->2248.3->3777.2 and so on continuing to exponentially increase as long as you have the infrastructure to support continued growth.

It may be lower if the efficiency of the recyclate becomes 60%, such that 168% * 60% = 100%.
Unfortunately, it would make shredding uneffective without production modules, plus a couple of beacons can make it more than 168%.

The other way is to make a separate furnace for recyclate, which is not really convenient :\

Er vanilla beacons cannot use production modules, that being said the 168% can be boosted depending on the products in question.

The 168 comes from a 3 step process Iron (+40%) -> Iron Sticks -> Iron Recyclate (+20%) -> Iron Plates

If you use for example flying robot frames 100 Iron plates invested for iron gear wheels will be boosted (excluding the other materials) up to 460.992 an increase of just over 360%, even if your shredder were 60% efficient you'd still end up with 230.496 Iron Recyclate just from the initial iron used for the iron gear wheels (100 Iron Plates)

This even affects your lower tier furnaces too even at 75% efficiency with a 1 step 40% boost you'll make gains of 5% much smaller then the other numbers but it will still add up over time, especially will multi pass intermediates.

Unfortunately I think the only way to fix something like this would be a clunky solution and not very compatible with other mods (as opposed to recycled standard components) would be to have special recipes that use recyclate instead of plates (and have the recycling furnaces produce recyclate too) that cannot benefit from production modules and can't be used in recipes that would benefit from production modules.

So no intermediate products or products that can be used to build intermediate products (like pipes) this would be ok for iron, copper and steel, but really bad for plastic as it'd would only leave tank shells as viable recipes.

Unfortunately I think the only way to fix something like this would be a clunky solution and not very compatible with other mods (as opposed to recycled standard components) would be to have special recipes that use recyclate instead of plates (and have the recycling furnaces produce recyclate too) that cannot benefit from production modules and can't be used in recipes that would benefit from production modules.

So no intermediate products or products that can be used to build intermediate products (like pipes) this would be ok for iron, copper and steel, but really bad for plastic as it'd would only leave tank shells as viable recipes.

I see, then it would stay recycle 'everything', just not 'make' everything with it. Currently you can hook up the recyclers to the main bus, with the regular metal plates, but otherwise you will end up building separate assembling line...
It will work with other mods though, as the recipes and items are generated on start up.

I think it would be fine to have recycled versions of wide-used items, such as belts, poles, chests and inserters. For example, 'Transport belt (recycled)' is made of 3 iron recyclates, 'Medium electric pole (recycled)' is made of 2 copper and 2 steel recyclates.
This would work nicely and without production module issues. (though still no use for plastic)