It’s the opposite. Higher rates of gun ownership are correlated with higher breaking and entering rates. Regardless of the relative economic status, location, and general crime levels of the areas looked at.
It’s also long been established that fire arms are both one of the most commonly sought items in burglaries and one of the most commonly stolen items in break ins of all kinds.
Gun ownership per capita is also inversely associated with population density. It’s known that the scary “large cities” don’t have nearly as many guns as the quiet suburbs.
More anecdotally, if you pay attention to this sort of thing. You run into a lot of reports of thieves deliberately targeting an area or house because there are known to be guns there. And there seems to be a bit of a trend in groups targeting affluent, white areas where cars and houses tend not to be locked specifically to find guns, because that is the sort of place you find them.
It’d be a bit impossible to prove causation. But it seems like a pretty good bet that if some one does break into your home. They are hoping to find a gun there.