Can Basil Self-seed?

A couple of years ago I bought several different types of basil seed from you. Last year I still had some seed left and grew it. Today when I was out weeding where the basil had been I saw what looked to be basil coming up in the area where I grew it last year (but did not plant it this year.) Is it possible that it self-seeded and the seeds survived a Minnesota winter? I looked at a couple of web sites and the only one that discussed it was a message board that had conflicting posts. In case it makes any difference, judging by the smell of the leaf I broke, it was either sacred or spice (I can't remember which had that particular smell.) Also, I have something growing that may be purple basil (or amaranthus that I planted in the same area, or a weed.) It did not have a smell when I broke a leaf open. Could that be basil too? I did not pull them, in case they were "volunteer" basil?

Winters are not what they used to be and some recent winters have been downright balmy. Also snow-cover can make a big difference. If snow falls on unfrozen ground it can keep all but the surface very close to freezing for extended cold spells.
Basil seed, unlike the plants, can take a bit of frost. Luckily, or we could not ship the seed all over the world!
If you have a long growing season, then basil can certainly self-seed. You will find though that it hybridizes very readily and the resulting seedlings will be a mix of their parents. It is also possible that some of last year's seed ended up too dry to germinate, survived a relatively mild winter and came up now, because they now are nice and wet.
If your purple plants do not have a smell, they are not basil, but probably amaranth, a seed that needs light to germinate. Any seed that was buried too deeply last year might have gotten to the surface this year and germinated.