Unfortunately, I have more septic knowledge and experience than I would like to have. I have an apartment building on a 1,200 gallon septic tank system with a lift station that I now maintain myself for 15 years.
In septic systems, it is bad when the sludge accumulates and gets out through the baffle into the drainfield where the solids fill-up the spaces between the soil and prevent the water from seeping or spreading out.
Sludge is controlled by either beneficial bacteria or by pumping it out. (by the way, the iron housings of the pumps don't rust because there is no oxygen down there--yikes)
The question is whether the ferts would encourage (probably) bacterial growth or kill the bacteria (unlikely). If it encouraged growth that would be good, but little or no appreciable benefit since it already has all it can eat.
If it killed the bacteria, that also probably wouldn't matter since new bacteria would be introduced by the solid waste drain and from human contributions--it would grow right back like a cycled fish tank.
Who really knows with doing some testing, but most likely one dump of ferts wouldn't make any difference whatsoever. If it were done on a regular basis, you may need to pump the tank a little more often.
A septic tank is a powerful thing and its doubtful one quart or so of anything would affect it at all.
Are you sorry you asked?