sure, definitely bring it up to the sound guy, but if he comes to the same conclusion as i did, he may recommend the same remedy, if not try to sell you more. if this is indeed the problem, all you should really need is an amplifier.

the amplifier will just take 12.6 volts from your battery (the same amount as a cigarette lighter or your radio/CD/cassette player), and create more voltage out of it to supply your speakers with extra power, which would drain less power from your head unit (radio/cd player). adding the clarion head unit like you are planning may not help entirely, though it could. 45 watts per channel isn't too bad, but that is most likely its peak power. so that means it can pump out 45 watts per channel at given times, it doesn't give any indication of conserving energy.

what the sound guy may try to sell you is a capacitor, and all that does is store energy when it is in surplus and put it to use when the power starts lacking. this may just add cost and not help a whole lot. see if he is nice enough to hook up an amplifier to your car as a test. it shouldn't take more than 10 minutes if he is experienced, especially if the dashboard has already been taken off since he is installing the Clarion. see if attaching the amplifier works to your satisfaction. don't go too pricey though.

hope this helps