Is it possible for a Navy vet to re-enlist into the Army (specifically 11B infantry scout) and maintain rank (E-3)?

You need to talk to a recruiter

Just a FYI, don't be too disappointed if the answer is you lose a stripe. You make rank in an Active Duty Infantry Company faster than anywhere else in the Army because they traditionally waiver promotion requirements because it is a tough MOS and with turnover they WANT TO PROMOTE good people fast. So don't freak if they say no. Past NCO experience your probably going to zoom up the rank hierarchy. I was a Private twice in the 1980's due to NG to Regular Army transfer rules, yes it sucks a little bit but you are also a lot more proficient in the MOS that way as well. May 1984 entered Active Duty Infantry unit as a E1, 15 months later I was an E4. College helps too.... and back then I just had 1 year of college. You get generally two promotion waivers E1-E4 TIS/TIG and they generally do not waiver to E2 because it is only 6 months. If your enlisting in the National Guard, promotion is slower and based on slots available.

I know a gentalman that went to basic training with me he was prior navy is rank was what every a E-6 staff sergeant is in the navy they let him keep his rank but like I said you need to talk to a army recruiter they are the ones that ask you if you at prior service to recommend you for rank