Criminals who burgle frequently go armed already, perhaps not with guns but certainly with screwdrivers etc.
I would contend that firearms are a great 'leveller'. Assuming both burglar and home owner are armed with the same weapons, a 60 year old home owner hasn't much chance against a 20 year old burglar if both are wielding knives, but if both have firearms any physical advantages in terms of strength etc. are immediately lost.
I'm not sure you know.
The burglar is already a desperate animal. Let's assume he's so desperate that he will attempt to rob you whether he thinks you are armed or not.
Now, if he thinks you aren't armed, he is probably less likely to get trigger happy should you come face to face. He has less to fear from you, and really, you don't want this person to panic or flip out, do you? He's just there to rob you, presumably he really doesn't want to kill you.
On the other hand, if he thinks you're armed, and he wakes you up and there's a confrontation, what are the chances he'll shoot first just to make sure he doesn't end up dead himself?