Assuming an interpretation of Battlefield Presence that allows you to keep Stealth Synergy up like this, there's certainly nothing to prevent you from using that swift action. It would work for your allies; for yourself, it depends on whether your GM takes the permissive "action tally" or restrictive "action pool" view.
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It should work just fine if for no other reason other then the fact that in most parties that won't work at all.
It is extremely difficult for an entire adventuring party to sneak up on anything as a group given most PC's aren't even trained in Stealth let along put a point in it. Even with a good roll in most situations you'll have someone below a 10. An this doesn't even take into consideration how infrequently most adventuring parties tend to not be the ones being ambushed or the fact that for it to work you'd have to end up going before everyone else in your group or they'll be left out. A rather large amount of investment into maybe getting a little more out of a surprise round.
If your party was built for it specifically and you figured out how to use it all the time then your getting into territory where your going to annoy your GM with a 'combo' and cause some additional hindrance to the enjoyment of everyone at the table. Be careful with something like that. Your GM may just say that it's too late to be effected by Lookout as well.
You'd likely find just giving everyone Lookout all the time with your battlefield ability might be more useful overall.