Coralline algae needs to be "seeded" somehow. I think what the OP is looking to achieve is essentially a FO tank. No live corals, no live rock, but faux everything.
It's not my cup 'o tea, but I won't judge.
If the OP does not add ANY live rock, or introduce any other natural items (corals, etc) that may have coralline on them, then no -- he probably won't have a problem with the purple stuff.
Just so you know, though -- a tank like this is going to require a high-end filter and consistent water changes. One of the benefits of live rock is the filtration it provides -- the rock has a lot of porosity for nitrifying bacteria to grow on it. I believe foam has some benefits for this as well, but IMHO nothing really beats out live rock in this regard.
Now to your other question about the floaty foam: Most people weigh their foam structures down with...
....wait for it.....
Live Rock. Maybe you could use some dry base rock instead....would that still be unappealing to you?