One thing I'm liking about new technology are these automated propane lockers. We have about 5 within a 10 minute drive. Sure, you might not get the best deal, but I'm usually on a tight schedule and the chatty hardware store guys get on my nerves. I, too, have three tanks in cycle. One's usually hooked up to the smoker, but since it doesn't burn much, it's a reliable backup.
As for affects on your beer, you'll need to run some tests, I think. You might find a new brewing process. Heat-bursting?
When I run out, I usually add another 5 or 10 minutes to my timer. I figure that it stopped boiling before I noticed it being out or it at least wasn't at the full boil.
I think this pointed me toward a replication problem I had a year ago. It was the day after Christmas and besides brewing in a <10F snowstorm, I'm pretty sure I ran out of propane mid boil and spent 15 or 20 minutes digging another tank out. I wasn't able to get the same recipe to come anywhere near the profile I had for that brew. Maybe I need to try a split boil to see what it does.