this conversion... is this something that I am going to be able to do in the background to ensure that things are functioning properly before flipping the switch to full SMF?
not really. just convert . go for it..
just in case, take a backup of your previous forum and your database.
SMF won't touch your phpBB forum, if somehow the conversion goes wrong your phpBB will still work perfectly.
I recommend locking your phpBB so that the conversion can be complete. If people post after the conversion is happening SMF won't have a complete copy.