I suppose you could do that, but we're only talking about ~8 oz (give or take) of bourbon for a 5g batch, so you may not get full submersion of the oak in a large vessel. Also, I've found that the vanilla will clump and can result in floaties if not filtered first. Whether or not it is an issue is really just personal preference. I like to filter it out once the flavor has had some time to transfer to the liquor. Another benefit to adding the bourbon to the beer at packaging is that you can hold some back (like maybe half) and then add more to taste if needed rather than committing to the entire amount, which might give more flavor than desired.
There's no single right way to do it. I've done it using a couple different methods and I've found that I prefer adding the liquor at packaging. YMMV.