Do canker sores in mouth provide a direct access to bloodstream ?

Minimal: Since the tissue is supplied with blood, you can expect that they are connected . Since canker sores are not likely to be from an infection per se (vs cold sores), they will not cause systemic invasion.

Not really : Anytime you have bleeding you have direct access to the blood stream. This includes biting your cheeks or tongue, periodontal disease, and cuts on your skin. Unless you cause addition trauma to the canker sore and cause it to bleed, you DO NOT have direct access to the blood stream.