When an item with an equipment grid is transferred by a connection (Inbound & Outbound) the equipment and any personalization to that item (like Spidertron label & color) are lost. I've only tested it with un-modded Spidertrons and Power Armor MK2; the results were the same for both.
While I'm not transporting Power Armor through connections, I do use Equipment Gantry (https://mods.factorio.com/mod/equipment-gantry) to automatically setup new Spidertrons. I can still do this inside a factory building, but I can't transport the Spidertron's outside the building without losing equipment. It would also be cool to be able to send Spidertron's with equipment back into the factory for equipment removal using Equipment Gantry's Removal machine.
I noticed in connections.chest.lua that ierms are inserted and removed using SimpleItemStack, which makes sense as almost all item's can be adequately described with this object. The problem though is that while an item is transferred, attributes like grids, inventory, customizable names/colors, and so on are not. It seems a LuaItemStack is needed in some way for transfers like these, but I couldn't test it as I only have limited experience with Lua and the Factorio API at this time.
Although transferring complex items via factory connections isn't a common use-case (in Vanilla-ish playthroughs at least), it would be awesome to see it supported in the future.