Yes, they count as vessels (unless you're in an odd place like the UK that decided many things don't) but whilst they're mentioned in the "lights and shapes" section of the rules, they're largely neglected by the "steering and sailing" section.

For example, sailing vessels have Rule 12 dedicated to them ("When two sailing vessels are approaching one another...") and the crossing and head-on rules are explicitly applicable for power-driven vessels ("When two power-driven vessels are crossing...").

The USCG's take on the matter is that it would fall into the "special circumstances" case:

Although a vessel under oars may be lit as a sailing vessel, one should not infer that they are considered to be a sailing vessel for other Rules (i.e. Rule 9, 10, 12, 18 or 35). Ultimately, the issue of whether a vessel under oars is the give way or stand-on vessel would fall to what would be required by the ordinary practice of seamen, or by the special circumstances of the case Rule 2, and, the notion that they are less able than most other vessels.