It can't hurt anyway, it would only make it cleaner if anything if you don't trust the source, but filter it first and then bake would be the correct order (you can't draw with a filter on either, so you draw, then add filter put a new needle on then fill the vial, and you'll loose 2ml of juice in the filter so you take 2ml extra of plain sterile oil and push it through). If your just trying to burn a little BA then no need to filter again though anyway, but you risk losing potency of the gear by heating it, although it should be fine at 150-200 for 15 min.
So filtering will do nothing for the BA but it cleans the gear if your worried about it being dirty. I'm not sure if the vaporization temp of BA is less than 200 so baking may not do anything but
going over 200 risks destroying your gear.
All in all bake it for 15min at 200 and you should have no worries of ruining the gear but it might not do anything to the BA either, you'll just be back where you started

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