No, neither production nor speed modules make any sense at all for the Bio Gardens: They produce "purified air", but that's not an item, so the recipe actually has no result (amount = 0).
Productivity modules give you a certain percentage of the result as bonus, but x percent of 0 still is 0, so you don't gain anything. However, using productivity modules will still reduce speed (which is good), and it will increase energy consumption and pollution.
Speed modules increase energy consumption and reduce the time needed to complete a crafting run. Less time per cycle usually is good, because you can produce more in the same time. But the gardens work in a completely different way!
Basically, the gardens produce nothing while they are running, but they require some ingredients (water + fertilizer) for each run, and they emit a negative amount of pollution while running. So, if you put some gardens and miners or furnaces in the same chunk, the negative amount of pollution from the gardens will be added to the positive amount of pollution from the other machines, and the overall pollution amount for that chunk will be decreased.
Look at the figures: If you supply a garden 1 normal fertilizer + 50 water (I think that's the number, can't check right now), it will run for 40 seconds (producing nothing, but emitting a negative amount of pollution). If you use 1 advanced fertilizer + 50 water, it will run for 100 seconds (still producing nothing, but emitting a negative amount of pollution for longer time). Now imagine you put a speed module into the garden: The garden will consume more energy, but it will also take less time to finish a crafting run, so you'll need to feed it more ingredients to reduce the amount of pollution for the same time.
So, the gardens don't benefit from speed boosts at all -- but they would benefit from a slow-down module! Likewise, efficiency modules that reduce the pollution don't work. If you have a level 3 efficiency module, it will reduce pollution by 50% (i.e. by a factor of 0.5). Now, -45 pollution units/minute * (1-0.5) equals -22.5 pollution units/minute, so you'd be better off without the module. To get any boost at all, you'd need a module that would give you -45 pollution units/minute * (1+0.5), so that you'd end up with -67.5 pollution units/minute.
So, the vanilla modules may shine with all normal machines that (1) produce >0 items/cycle, and (2) produce >0 pollution units/minute -- but to achieve the same effect with the gardens, you would need slow-down modules and inefficiency modules.
It certainly would be possible to make these -- modules are just prototypes like anything else in the game. However, I wonder if that would really make sense! There would only be one prototype where it would make sense to use them (the Bio gardens). So for each module prototype, you'd get one more item that takes up space in the crafting menu but is useless in all entities except the gardens (you'd probably also want higher tiers of these modules, so even more slots in the menu would be wasted).
But let's assume you'd really want to module the gardens, there would be two possible ways to approach this:
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We could create a combined slow-down inefficiency module (possibly several tiers), and the gardens would only accept these. (We could base that on a setting that's off per default, based on the assumption that you know what you're doing if you activate that setting.) The modules would work only in our gardens (because we don't have any other prototype that works the same way, and it's unlikely that other mods would utilize our prototypes).
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I could create a new mod that provides slow-down and inefficiency modules (and/or a combination of them, perhaps) that would be an optional dependency of BI. This way, the new modules would get some exposure and could be used by any other mod as well, if necessary.
Would either of these be OK with you? I kind of like the idea, but if I were to implement it, it would probably be in a later version, not right now.
