A budget power amp, yes.
A quality power amp, very very minimally.
Any amp (or component, cable, bass, pickups, speaker wire, stage construction, tires on your gig vehicle...) will affect your tone in some way. You wanna find an amp that affects it the LEAST.
I know most "affordable" PA power amps do a good enough job. But if you're getting a power amp just for your bass rig, it's wise to spend the money and get a quality power amplifier. Yes, all power amps can reproduce those low frequencies, but not all of them do it well. That means, not all of them will get those 35hz frequencies out as loud as it could the 80hz frequencies. The really lower-range fidelity is in question when spending $300 on a power amp just for bass. So look into the QSC PLX series amps. Yes, a pretty penny. Yes, excellent quality and sound reproduction. No, no serious or annoying coloring of your tone.