If your main motivation is to get her some socialization time, then yes, I think play-based makes a lot of sense. As I mentioned, we needed full-day care -- our Montessori preschool was 5 mornings a week, and they had "extended day" until 5:30 when those kids continued their works.
I took a semester off of school and had ds-then-3 in a simple community center play program for 2.5 hours, two mornings a week during that time so he didn't get out of the swing of going to "school." It sounds like something like that may be what you're looking for -- there is more freedom for play and she might prefer that.
OTOH, if she is worried by other kids, she may prefer the quiet, structured atmosphere of Montessori. Really, the only way you'll know is by taking her in for a visit!
One thing to consider ... parallel play, where kids play the same thing but alongside each other, not interactive, is very, very normal at that age. Even if she knew the kids, she may not be interested in interactive play, *especially* if she's noticeably ahead of where they are cognitively. They might not understand her games or want to do what she's doing.
DS-then-4 didn't interact much with the kids at his play-based childcare; they just didn't share his interests. He did meet some more kids that interested him at his Montessori -- I think there were more G kids there, though I'm not sure why that is. Just keep in mind that she might not experience the "shared play" until she's a bit older, whether she's in preschool or not.
That said, I think there is a lot of value in the "separate from mom" time that kids with SAHMs get from play-based school, gifted or not, for all the reasons you've listed -- comfortability with other kids, being okay with mom leaving for a bit and knowing she'll come back, social skills like sharing and waiting. Go and observe!
I think some of the selfishness is also me just not wanting to deal with what most parents have to deal with when there child goes to school. How do I check on her and make sure everything is ok, what if everything isn't ok, what if somehow my choice of programs for her has in some way changed her in a negative way.
This I can answer, because I was an infant teacher for two years (and loved it!). You can call to check on her. You can ask for a written report each day. You'll know if things aren't going well from her general attitude.
If you do decide to take the plunge, it may take a short adjustment time before she really enjoys going -- I'd give it 6 weeks, whether she loves it or screams at drop off every morning, before making a final decision on whether to keep her in or pull her out. Being away from mom can be a big adjustment for a kid with a SAHM, so give her some time to get used to the idea if she isn't keen on it at first. But you'll know if it's not going well, and you can always pull her out if it's truly a disaster.
Likely, though, she'd enjoy it!
