Hi, @Steven Dome. In theory, you can use your HELOC money on anything, so yes you could use on a downpayment for a BRRRR.
With that said, finding BRRRR-able properties isn't easy. Part of the process is finding undervalued properties and forcing equity through rehab at such a velocity that you can take out all or most of your initial investment. One of the easiest ways to secure an undervalued property is to pay for it in all cash (either your own cash or via Private/hard money). Many properties that are undervalued are in such disrepair that you can't get a traditional mortgage on them in the first place, plus you typically can get a better deal on an all-cash offer. Just something to be mindful of.
Yes, some lenders will allow you to build renovation costs into the loan. I have one guy that I work with in Michigan who does that. No clue if his bank does properties in PA, but if you DM me, I can share his info.
Assuming that you're able to get all of the above to work, just as with the HELOC, you can do whatever you want with the funds derived from a cash-out refi, so in theory you could pay back your HELOC with those funds. Of course, you want to pay attention to where you have the more favorable interest rate, though, before you do that.
Regarding the "waiting period", that varies from lender to lender. Some require a "seasoning period" where you need to hold the property for 3 to 6 months before you can refinance. Others don't require a seasoning period at all. Really depends on the lender.
If you live and invest in PA, I suggest compiling a list of every credit union in your area, call them all and see about the terms they offer. Everyone has different policies.