Audio Systems: crossover, power rms, rms voltage

Question
If I am planning to install a 50W system in a car and use a 600W (it is not stated if this is RMS or not) 120Hz crossover for the sub (which will also be operating at 50W) will this affect the performance in any way?

Answer
Should be no problem, but I would need to know the make and model of the products you are referring to in order to give you a for-sure reply.

When you say 50w system what does that mean?  A 50w power amplifier?
When you say 600w crossover what does that mean?  Are you using a passive crossover.
Why are you using 120 Hz crossover frequency?  That is quite high isn't it?
Why are you not using just RC crossover into the input of the sub amp?  Or, why not us a sub amp that has the crossover built right into the input of the amp?  Or, why not use a self-powered sub with amp, speaker and crossover all in one?

Sorry for all the questions, but I am trying to guess what you are doing and why.  Let me know if you wish to discuss further.

C

PS: And, by the way, there is not such thing as RMS power. RMS is a voltage or current term; when RMS voltage is multiplied by the RMS current it yield AVERAGE power, not RMS power. I know everybody uses it but is is wrong, wrong and wrong.