Angel food is different than most cakes in that it needs the ungreased pan surface to "climb" up to get it's light, airy height. This is why a tube pan is used, so the center also has a surface to "climb" up.
I've never tried making one in a regular pan, so I can't say if it will work or not. But I suspect you may end up with a cake that is higher around the edges and sunken in the middle.
If you use a heat core, it would only help if it is ungreased. And I'm not sure it would then be easy too remove without destroying the cake.
Hm. The last "white" cake I tried to make came out like an angelfood cake, and it was baked in an 8" round pan. It was a BEAUTIFUL angelfood cake. The only problem is that it was 'sposed to be a white cake. 
(Not helpful, I know!)
Seriously though, I really don't know much about the specifics of angelfood cakes, but I thought the purpose of the tube pan was to be able to flip it upside-down to cool. (Otherwise it would collapse...?) And that you're not supposed to grease the pan so that the cake can cling to it as it rises and settles. EDIT: As I was typing this, I saw artscallion chime in, confirming what I was thinking. WOO-HOO, I feel so smart! 
It seems like it would work to me, as long as you didn't grease the pan and were sure you could get it out after it was baked. I'm thinking a springform cheesecake pan, maybe. Something that disassembles so you can slide a knife under the bottom, ya know? I would give that a shot. A springform pan with a few flower nails instead of heating cores. It seems like those would be easier to remove, ungreased... ?
I'll shut up now, since I don't really know what I'm talking about, and my mad-scientist logic backfires all too often. 
I think if you want an angelfood cake, you should buy a proper tin, the tin is nice and tall and has 'feet' because you need to turn the pan upside down to cool the cake, and if you do get a tin, don't get a non stick one, they're not too expensive. Angelfood cakes are sooooooo good 
Today I took the cakes that I made in 10" round regular cake pans and put strawberry cream filling in them and stacked them up......they worked prefectly!! I covered them with Rich's bettercreme....put the dowels in and it worked......wow, all that worry!!
I make many layered angel food cakes with regular round pans for wedding cakes or birthday parties.
1) Do NOT grease the pan
2) Put a piece of parchment paper in the bottom
3) Depending on the size only bake 20 - 30 minutes (until toothpick is clean)
4) Cool upside down on a rack for 1 hour then remove pan and parchment paper
5) Cool completely
6) Decorate as usual, using dowels if stacking for a tiered cake.
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