I'd pop it in without fear and see how it sounds.
It is true that the 5U4 draws 3 Amps compared to the 2 Amps of the 5AR4, but its higher internal resistance is easier on the power transformer, so the total flux dissipation in the power tranny won't increase. However, you will lower your voltage an your power by doing this. That will be GOOD for tube life, offsetting the mildly faster warmup than the 5AR4. It will lower your power output, probably not the main reason you have a tube-amp, but... The input cap in the power supply should not exceed 40 uF for either a 5AR4 or a 5U4, so that should be no problem.
One of the scrimpiest power transformers ever, on the Dyna ST-70 was made for a 5AR4, and I got one 34 yrs. old with the original tubes all still working, sporting a 5U4GB that the original kit builder had substituted at the outset. Good arguement to dive-in, I'd say...
John