Sending to GY a monster that can't be targeted
Will the effect resolve and send my monster to the GY or not?


It will really help if you mentioned the specific card.

However in general terms, as you describe it, the effect will resolve, and send the card to your GY.

This is because, based on your description, such card does not target (you select it) nor does it destroy (it sends). Again, it will help to know the exact card to be 100% sure.