Oh, I doubt that. In BJJ, you spend the majority of your time either defending guard or passing guard. A pure striker, with no BJJ training, isn't going to be able to prevent a BJJ expert from passing his guard. My guess, with all due respect, is that you're misreading what the fighters specialize in. Usually when someone can maintain guard, they've spent a lot of time in BJJ. The guard is actually the staple of BJJ. And when someone can't pass guard, they just go ahead and beat the guy down.
And to answer your question, that's the real danger of having someone in your guard. It's not simply a matter of not letting them pass. You have to keep threatening with submissions and prevent then from striking you. In the words of Caesar Gracie, "Take a Jiujitsu black belt and punch him in the face once, he's a brown belt. Punch him twice, he's a purple belt". So avoiding strikes, especially when your head is backed up by the planet, is of primary concern.
If you don't train BJJ, you're not really going to have a good guard. You won't have put in the time it takes to develop skill at controlling your opponent and actually working the guard. The guard is, at best, a neutral position. Half guard is even less advantageous. Only the premier BJJ guys can defend themselves from that position in an MMA type situation. Again, it's not so much subs you have to worry about, it's getting your head caved in.
But with no training, could you prevent subs? Not really. From guard, you're susceptible to leg locks, and just about nobody, especially a newbie, can adequately defend leg locks. Plus, you have to worry about a few arms and neck locks, the most obvious being the "can opener". Without submission training, you won't know how to defend them.
To defend submissions, you have to understand submissions.
Edit: right, no submissions from inside the guard, huh?
http://www.youtube.com/watch?v=Idau2AjsU70
http://www.youtube.com/watch?v=FzCUHjPJz04
http://www.youtube.com/watch?v=0lOEZwv0CoM
(see about 1:50)
Two leg locks and a neck crank. I get leg locks all the time.