No. That's only a 4.8% increase in your top gear. By comparison, if your two smallest rear cogs have 11 and 12 teeth, that last jump with your current gears is an increase of 9%. So moving to a 44t chainring would be like adding only a half gear more.

What pedals and shoes are you wearing? Do you have any idea what your cadence is? I would expect your top gear to be about 99 inches, which would put you over 26 miles per hour if you spun at 90rpm. 26 mph is plenty fast for most commuters (double what many of us average). If your 99 inch gear isn't enough, I think your first step is seeing if you can increase your cadence -- it sounds like you're either very strong with a really fast, clear route or you're not spinning the cranks very quickly. Clipless pedals and cycling shoes are IMO the easiest way to facilitate spinning.

It would make more sense to replace your crankset (which I assume is something like 22-32-42) with a 26-36-48 crankset (plus get a correspondingly longer chain) than to merely switch to a 44t big ring. Moving to 26-36-48 would increase your top gear by 14.3%, nearly as much as adding two higher gears.