Nope, FSD Beta is only for the City Streets function, which is a L2 system. When it is out of the limited beta, it'll be to deliver the "Autosteer on City Streets" bullet point on the current order page. It will not be the features that were promised in earlier FSD order pages that suggested L4. I actually discussed this before with you, with reference to the DMV filing that explained it.
FSD Beta Videos (and questions for FSD Beta drivers)
I also gave my analysis of the 3 different stages that Elon talked about in the past. City Streets (end-to-end L2) can basically be released when it's "feature complete". This does not require 200% better than average human, only basic competence in day-to-day local driving (such that it's a feature rather than an annoyance, for example, it currently failing more than or approaching half the time on fairly basic tasks like unprotected lefts is not competent enough yet).
Stage 2 is L3+:
"feature complete to the degree that … where we think that the person in the car does not need to pay attention"
Tesla was clear in the DMV document that "Autosteer on City Streets" will be purely L2 on public release and not L3+, so it's not going to match this criteria.
Elon thinks that after reaching "feature complete" that it'll be only a matter of gathering data to improve reliability to reach L4/L5, which is likely not realistic (at least in near term time scales), so I don't see Tesla holding out releasing City Streets while waiting for that goal. Their filing with DMV suggests they would release City Streets first before they move to the next step of L4/L5 development.