I don't think we need to worry about it, no... migrations to Beta sites (or away from them, for that matter) require moderator intervention on the originating site, which means that it's pretty simple to get the migrations to stop by having our moderators ask their moderators to stop migrations.
While we don't yet have any pro-tem mods, I have gone ahead and asked the moderators on ELU, for the time being, to not migrate questions here. We had three questions migrated in a short period of time and two of them have been rejected in pretty short order with the third sitting at four close votes as of this writing. In general, migrations to beta sites, particularly early beta sites that are still trying to figure out their scope are discouraged.
It's much preferred that sites close the question there and direct them our way for a few reasons:
Users will likely not have an account here and may not wish one, which means their question may be abandoned if they never appear here to respond to requests for clarification.
Questions that are put on hold/closed (other than as a duplicate) are immediately kicked back to the other site which means we can't put them on hold to prevent answers while waiting for more information - something we can do with questions asked natively here.
Any answers already on the question may not be written with the framing appropriate here and the users writing the answers may have the same issues as the askers in point #1.
So, while I'm not saying we should ban all migrations - I think the moderators at reasonably similar sites like Parenting or The Workplace may be easily able to learn our guidelines and be respectful about migrations - we should check in on migrations from other sites that seem to be repeatedly missing the mark and discourage them through the mods directly.
I hope no one believes I'm overstepping to address it in the interim. I did mention it in chat and had two users agree that it should be addressed, so I did.