I ran into this too. My 2 cents is yes - but it's not very effective. First, you're doing the wrong kind of damage - social stress doesn't stack with physical stress. Second, you need to consider the consequences of a social conflict are not as desirable in a fight with a physical creature, accept in certain circumstances - e.g. making an ogre start to stutter in the middle of a fight wont really help you hurt it - unless you can convince his friends to turn on him of course...
The end result? It's better to use social skills to place aspects rather than attacks. But on the other hand, if everyone else were to layer on the aspects and the social charactor used them to launch one massive social attack, it'd be effective, if not thematically awesome.
E.g. There's a big old ogre in front of our wily group of adventurers. Our group doesn't think they can take him in a straight on fight, but they figure he's more gullible than weak (he has more social stress than physical) so, when Hero A gets his turn, he places the aspect 'flanked!' on the ogre. Hero B places 'uneven footing' on the ogre, Hero C puts 'outnumbered on the ogre' and Hero D, being the social monster, uses all the aspects to launch a 10 social stress attack on the ogre. This is repeated and the ogre is convinced to surrender in a turn, convinced he can't possibly win and he should probably just give in and help them instead of trying to fight it out. The group sighs a sigh of relief: they've effectively circumvented the monsters toughness powers and formidable strength and finished a massive fight in 2 rounds. The GM grins, this is actually a pretty cool result.