If that were to happen, there might also be an impact in the tank itself (causing a backup as you note). But that might not happen for some time (as sludge builds up) and, depending on frequency of pumping out the tank, possibly never known. Meanwhile, you may not be effectively treating the effluent.
I haven't been able to find definitive info on photo chemicals and septic tanks. Lots of discussion and anecdotal experience on APUG (and elsewhere), but little hard data. Kodak "does not recommend the use of septic systems for disposal of photographic processing", but years ago they said it was OK. Who knows whether it's driven by science, more concern about groundwater, or the lawyers?
A lot of variables. If the OP is sending all his other "common" contaminants (bleach from washing machine and dishwasher, antibacterial soap) out as grey water, the impact of the photo chemicals may be less significant. But if his septic tank is small (reflecting the separate grey water system) there is less dilution.