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Most likely yes. The only reason to have separate amps for each output would be to reduce distortion in a high level amp, which will not be the case here.
Warning - some of the cheap amps are not very good, tend to provide more gain than needed (on the theory that people will think more is better), and can have a tendency to oscillate. I had a RadioShack one that would oscillate, and the frequency would tune through the UHF band as you adjusted the gain. You could see this on analog TV as a herringbone pattern in the picture, but on digital, it would be hard to tell why you might be clobbering a particular channel's signal.
I'm not prepared to recommend a particular brand - our expert is out at CES, so I can't ask him right now.
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