Roy Tang

Yes, first the active player gains priority, then when he passes the non-active player will receive priority. This happens regardless of whether triggers go on the stack.

Comp. rules:

503. Upkeep Step

503.1. First, any abilities that trigger at the beginning of the upkeep step and any abilities that triggered during the turn’s untap step go on the stack. (See rule 603, “Handling Triggered Abilities.")

503.2. Second, the active player gets priority. Players may cast spells and activate abilities.

116.3a The active player receives priority at the beginning of most steps and phases, after any turn-based actions (such as drawing a card during the draw step; see rule 703) have been dealt with and abilities that trigger at the beginning of that phase or step have been put on the stack. No player receives priority during the untap step. Players usually don’t get priority during the cleanup step (see rule 514.3).