How to determine if canning is safe?
In regards to your particular tomato sauce. I don't think its acidic enough (a pH of 4.6 that is), and according to this page - the answer is no.  Even when canning fresh tomatoes or other tomato sauces you need to add some lemon juice.  Now you could try lowering the ph, but it would drastically change your recipe probably - whether or not you want to do this is up to you.

If you have a pressure canner, you likely can do it.

Generally, yes - it is a function of temperature and acidity. You need to either sterilize the food through temperature, or create an environment in which the bacteria won't grow - normally a higher acidity.  Pressure canners work by sterilizing, so recipes that are low in acid can still be canned.