If the stolen goods are identifiable and turn up in some way, you may get some progress. Or similarly if the pattern of crime suggests it is worth their time trying to catch a prolific offender. Or if the crime is more severe than quotidian offences. But typically the crime number allows you to make your insurance claim, it gets logged in the police crime database, and that's all that happens.
My evidence is the experience of myself, friends and family.
Apparently my neighbor heard the guy shouting "Fucking foreigner" (we both had foreign registration plates at the time) or something similar and reported it. Apparently, that moves the crime into the hate crime category and warrant extra police work. So even though I didn't report the slashing, the police came to my place to gather my version.
Overall same result though and I wasn't really expecting any result to be fair.
If your low-priority crime (like criminal damage) can somehow be placed in a higher priority category (like hate-crime), the police will find it much easier to allocate resources to it, and you will see a more spirited investigation.
My original point was merely to say that there are such things as low-priorities for which the police don't put much effort, and by doing so they set a precedence for what crimes one could reasonably expect to get away with.
The published data shows that only a tiny minority of petty crimes end in conviction, however. In my experience (5 times, including family and close friends), the police chose not to send an officer to the scene.
I'm sure some petty crimes get solved, and some serious crimes don't. But if you thought I was making either point, may I respectfully suggest you reread my comment.
So on that basis, the likelihood is > 95% that you'll get away with it.
And note that those statistics are for all burglary, including aggravated burglary. I can't tell from the data, but I'd suggest it is reasonable to assume that petty burglary has a lower conviction rate still.