This is a good strategy OP if you are looking to save $$ and/or want a neighborhood experience.
Keep in mind though that it's quite difficult to get into Potomac in 3rd grade (if your child doesn't make AAP) as its not an entry year. That means no new seats in 3rd are added (so you will be stuck for at least 3rd in your neighborhood public). We've known plenty of people who were 'banking' on Potomac later year entry (i.e. 1st, 2nd, 3rd) and it did not materialize.
In order to secure a 3rd grade slot in Potomac if AAP doesn't work out, you'd be betting on a Potomac 2nd grade family to transfer their child (unlikely unless a move), and that of all the applicants for that spot (including siblings) your child gets it. Those are not great odds.
If your child didn't make the cut for AAP likely his/her test scores were a factor in that screen. Potomac requires similar tests so your child will be competing with those who may have scored higher (it's not the only factor but when there are only a few slots, it does play a role).
As long as you would be ok potentially staying in public for a few years if your child doesn't get AAP, then you'd be good to try it out.
Of note- things open up for Potomac in 4th (it is an entry year with about 15-20 slots), but, it's also pretty competitive (and you are competing with siblings/alumni and some transfers from AAP with potentially high standardized test scores).