Walter,
The listed draft on my boat is 4' but that's with a very lightly loaded boat, most times I figure at least 4'4" and fully loaded for an offshore fishing trip I'm about 4'10". Different companies list their drafts at different load levels so I would find out if that 3'10" is light, full, or somewhere in between.
Either way though it is doable on the bay. The main problem area I have is the entrance to my canal. My general rule is to avoid coming and going within 2 hours of low tide. A lot of times that's not even necessary if the tide is high enough (easier to tell when I'm at home starting out rather than coming back though). I'm pretty sure the entrance to the Anchorage is deeper though so that shouldn't be an issue except maybe on extreme low tides like after a stretch of strong NW winds in the fall.
I've had my boat 8 years now and am still on the original set of props. The only time I really did any prop damage was within the first month I had the boat and came in from an overnight anchored up when I should have waited. Even then it was a minor nick and I ran the boat the rest of the season without any issues. I have a slight ding now that I'm not sure when I picked it up, but it will be the first time in at least 3 seasons the props will be off the boat. My boat doesn't sit at the dock a lot, I normally put between 130-145 hours a season on the engines, and while a lot of it is long trips and fishing, i do a lot of local running around in the bay also.
I think the way you use the boat you'll be fine. When I had I/O boats I did more prop damage then because I used to explore different areas knowing I could always lift the drive and would end up bumping bottom a lot. Once I made the switch to inboards exploring random canals and going clamming with the 'big boat' became a thing of the past. That's what the dinghy is for

If you were coming out of a small day boat with outboards or I/Os and were used to running all around in the flats and cutting across the bay it would be a big adjustment, but you already have a fairly large inboard boat and probably don't do that now. For running out to places like Watch Hill, Sailor's Haven, or Hemlock Cove, or going to the inlet to head out on trips or running west to Jones Inlet, there really aren't any issues. You just need to stay in the channels, might have to wait a little longer coming out the canal to hit the throttles to make sure you're in deep water, etc, but if you're careful it's not a hard adjustment. Sometimes I wish I didn't have to work around the tides, but when you're going out for a weekend trip it's really not a big deal to have to leave a couple hours earlier or later if needed, and to me it's been worth the extra comfort of the bigger boat.
John