Yeah, that should be okay. If you're really worried about it, there are plenty of other oxidation options: Swern, Dess-Martin, TPAP/NMO....
All of those would be fine with a TBDMS group.
In your case, there is the possibility of beta-elimination to form acrolein. You might want to consider Dess-Martin reagent because it is probably the most mild oxidant of the ones that I mentioned, so beta-elimination would be minimized.