Sure! I think you can, if the circumstances are right for that.
Kezza summed it up pretty well. If one side still clings to the relationship, and can't accept only friendship, that can make it pretty awkward and probably not worthwhile. Plus, then it is an imbalanced scenario. Because the two are coming from different places. That can still work sometimes, but it's less likely to be fruitful for very long.
But sometimes friends is all that was meant to be, and as long as both parties accept that, then if mutual respect remains a part of it, it can work out very well. In fact I think that happens quite a bit. Situations like Seinfeld and Elaine for example. Not uncommon.
For me, it works better the other way around. Friends first, with the possibility of it becoming something more. Or not. But with nothing presumed in advance.
Mother Nature is pretty smart, and she's been doing this a long time. She'll work it out one way or another.
-RB