Elementary Tomato Canning
The reason that people talk about "proper" trusted recipes in canning is that with anything less than that, all bets are off. Might keep, might not.

That's definitely true of your suggested process: they might keep in the fridge that long, might not, and as a bonus, if you get unlucky, there might be nasty undetectable botulism in there! Tomatoes aren't quite a low enough pH to avoid that, boiling isn't a high enough temperature to kill it either, your process won't even seal the jars, and refrigerator temperatures don't stop it from growing. You're really just using the jars as containers; there's nothing about the process that's actually "canning". You'd get the same results from putting tomato sauce in plastic containers.

And, honestly, a proper recipe is not even much more work than what you're talking about. For example, here's a trustworthy recipe for canned crushed tomatoes, pretty similar to what you want. It's pretty much:


blanch and remove skins
cut into quarters
mash some of them a bit and heat to boiling
add the rest
add acid (citric acid or bottled lemon juice)
put in jars and process (essentially, boil the filled jars for the time specified in the recipe; exhaustive description here)


So basically, that's your process with the addition of acid, and boiling the jars after filling, and it will make them keep at room temperature.

They have a bunch of variations if that's not exactly how you want them prepared.

If you aren't willing to put in that much effort, then I'd really suggest freezing. That removes all of the safety concerns with no complications at all. You can just prepare however you want, put into hopefully smallish containers so you can get at a manageable amount without thawing, and pop in the freezer.