Op-Amp circuit analysis
You are right.

The calculations for the analysis of OpAmps are done assuming they are ideal. However, actual op-amps are not ideal and are limited by the Vcc supplied to them.

Take for example the gain in the following circuit -



Gain here is -(R2/R1).

So, Vout vs Vin should ideally be a straight line. But because the peak voltage in the circuit is limited by Vcc, the output voltage can never cross |Vcc|. Hence, Vout will saturate to Vcc.

Verify this on Falstad

This happens because the op-amps are not ideal in real life.

To answer your question, the opamp will try to behave normally as long as it does not hit the Vcc and when it does, that will give you the maximum current through RL.