[morzh]

Well, in a way.....transformerless radios are usually not heavy drawers.

However the sole criterion is: do not exceed any of your winding's current rating.
If your 6.3V winding IS a 20A capable one....sure! Use it!
But somehow I doubt this is the case.

Remember: a transformer is a power transfer (or impedance matching) device - it keeps the power constant plus the core and resistance losses.
So ideally, your 100 Watts travels across the two as 100 Watts, and in every winding it is the constant power. You draw 100 Watts from your 120V output, it is 0.85A in both input and output but it is 19.5A in between where you use 6.3V ones.