All the answers were great and I really appreciate it!
They all got me to thinking and I've come up with a new approach to my issue.
Originally, I was going to have my PHP script run the MAIL() function while the user waited. This poses problems of it's own... Like, what if the user shuts down their browser?
So, what I'm going to do is save the info to my database, and then run cron jobs every so often, looking for unsent mail. When it finds some, it will send it. With this approach, I can send important mail blasts immediately (or within a reasonable amount of time), and not-so-important mail in the wee hours of the morning as to not clog up my server. Then, after my mail has successfully (or unsuccessfully) sent, I can send an update to my user.
Thank you to everyone that responded! It was all the answers together that got my brain working...
Rick