Thawed frozen blueberries inside cake roll?
Yes, the blueberries will bleed, and, what's even more non-4th-ish, they will make purple or lavender stains instead of blue.

If you are serving the roll rather quickly after assembly, consider thickening the pureed blueberries seperately with some corn starch or pudding mix. Then you can make a blue-and-white filling inside the red roll. The blueberries must be boiled and cooled again, obviously, because they would otherways melt your cream cheese icing. Aim for a "spreadable pudding when cool" consistency of the berries, ideally the same consistency as the cream cheese filling.

You can layer both fillings atop each other, but the risk of  them mixing when rolling the log is high. I suggest piping alternating blue and white stripes parallel to the edge where you hold it / future long axis of the log and rolling very, very carefully. This should result in a blue/white pattern when you slice the log (wipe the blade often!).

The longer you store your log, the more colour will leach into the white, but a few hours should be ok. Chill thoroughly.