Will the ps3 demo for battlefield bad company 2 have online?

To put it simply, yes.

However, just like with the Demo fro the original game - BF BC - you can only play one level (Port Valdez) which is a large snowy level; you can only reach a certain level (once reaching level 2 it takes an impossible amount of experience to get to level 3); you can only unlock a limited amount of weapons (you start with 1 primary weapon for each class and can only unlock one more for each) etc.

I would say more but you can just find that ouut when you play it, I hope I helped.

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To sum it all up into three words, no it wont.