Is it possible to over-clean a bike chain?
Evidence, not sure.  I can say I've used the Park Tool chain cleaner, which is pretty much a bath, along with Simple Green solvent for years with no problems whatsoever.



It does completely remove the chain lube/grease, which is the point.  When I clean the chain I want all the old lube off, along with the grit and dirt in the lube.

As long as you remove the solvent afterward, let the chain completely dry, and then re-lube it, on every link, carefully hitting both sides of the link, you won't have problems or shortened chain life - you should have extended chain life.  

I've been using this method on a Sram 11 speed chain that's used as my daily commuter (rain, snow, city road grit) and it's like new.  The chain is 2 years old now. I should mention that I do clean it regularly and thoroughly, probably once or twice a month.