Tomato plants can certainly break under weight. Some varieties are more prone to breaking than others (e.g. Early Girl F1); I'm not sure about San Marzano, although I've grown it without issues.
However, you don't necessarily need to support tomatoes to prevent them from breaking. The plants just need enough potassium. Sufficient potassium makes tomato vines, leaves, and roots very strong and tough. Plants don't need as much potassium as I'm talking about to do well, but if you have weak plants, adding extra is one way to strengthen them (don't add extra nitrogen with it, however, unless you need it). Extra potassium may affect the flavor and texture (for better or worse), however. This is my experience. Plants toughen up within a few days of a good dose of potassium sulfate (even old growth).
I almost exclusively grow my tomatoes without support, and those I've given extra potassium have hardly ever broken. These days I usually use wood ash for potassium instead of potassium sulfate (since wood ash is fairly sustainable and has a wide array of nutrients, and tomatoes seem to benefit more all-around from it), but I believe potassium sulfate has a more potent effect in strengthening the branches and such.
When vines do break, if they're still attached at all, often they'll keep growing like nothing happened, as long as they're still somewhat attached. It's kind of surprising.
I'm not necessarily recommending that you go the extra-potassium route, since it changes the way plants behave considerably, but I wanted to point out that it seems to work as an alternative option.