It's about 1, 200 statute miles from Ft Myers to Norfolk. From Norfolk to Baltimore is about 140 nautical miles. The first section averaging 75 statute miles a day will take 16 days. The Chesapeake could be done in 2 days. So running every day and no weather days, 18 would be the bare minimum going inside the whole way.
If you feel comfortable with the new boat and your experience, going outside from Stuart, FL up to maybe Morehead City, NC will save you a bunch of days. You likely may not be able to run that entire distance outside, but weather in May could give you a 2 day window. Running outside for 36 hours (7am to 7pm) in the gulf stream (2 knot push) could be the equivalent of 5 or 6 days in the ICW. If it were me with a new to me boat, the forecast would have to be near perfect. Size, condition, and how the boat was outfitted would greatly influence my decision.
The days are longer in late May, so you should be able to average more miles per day inside. The tough part is having a place to stop each night. There are long stretches without anchorages that will force you to cut your days short. Wind is only a limiting factor in a few areas such as lake Okeechobee, Chesapeake Bay, and a few of sounds. How comfortable are you boating in heavy rain storms? Fatigue is another issue. 10 to 12 hours a day for 18 days is tough.
Answer to your question without knowing you, your crew, your experience, and of course the boat is a qualified yes it's doable. Post a link to the boat and tell us a bout your experience level.
Ted