Can an illegal target that will become a legal target before the spell resolves be targeted?
You can't choose to target an illegal target. Period. When the Harbinger of Tides enters the battlefield, it can only target creatures that are tapped at that time.

To be specific, the following rules are relevant:


603.3. Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority. [...]

[...]

603.3d The remainder of the process for putting a triggered ability on the stack is identical to the process for casting a spell listed in rules 601.2c–d. If a choice is required when the triggered ability goes on the stack but no legal choices can be made for it, or if a rule or a continuous effect otherwise makes the ability illegal, the ability is simply removed from the stack.

601.2c The player announces his or her choice of an appropriate player, object, or zone for each target the spell requires. [...]