Yup, fine. Just takes up more space and gets hotter in the middle because of all the insulation.
Can also connect them in series, if you feel like saving turns. (This has a high-frequency downside of increasing capacitance between turns, but that doesn't matter here.)
Multiple strands or builds are often seen at high frequency, to reduce losses; at mains frequency, there's simply no difference.
Mind that the primary uses a few turns less than it should, so the core runs in saturation and gets very hot under continuous duty. You may wish to add some turns of your own.
Also FYI, knock out the magnetic shunts, they make the transformer "worse"; which is good for the intended application but not helpful here (you'll be using a FWB and cap to make DC I assume?).
Tim