Probably not. The amount of flange movement in the axis of the beam for a "torsionally free" end condition is pretty small, so you need to be really stiff to effectively restrain that. Depending on your deck detail, that can be possible. But for your bottom flange, the fact that you have slotted holes (so presumably not slip critical bolts) means I wouldn't call that torsionally restrained.
I don't know the whole story, but you'll most often be best to find another solution that doesn't require your beams to be torsionally restrained.
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The name is a long story -- just call me Lo.