I've seen prams at all of my local events with varying degrees of success. You should check out the course description of your local events, it'll say something like:

parkrunners pushing buggies are welcome, but please take care of others around you and do your best to start at an appropriate place in the field for your pace.

I'd encourage you to head along, it's a blast, just be aware and respectful of those around you.

Would this not be reasonably obvious? How else is it going to track your sleep without this data/permissions?