That's one way to look at it, but I don't know that I'd call it reluctant. Absent minded maybe. Data's ambition, if there even is any, is easy to overlook, even for Picard, which is maybe another reason Data languished in the ranks for 2 decades. It's easy to pass over the man who makes no noise about it.
I can't see Picard deliberately passing over Data for a ship on competency grounds though. He's one for giving people chances, even a kid like Wes, or a problem officer like Barclay, when others wanted him transferred. In a weird way, The Enterprise is full of people Picard is trying to provide some amount of just dues.
Which is odd to me, because some officers like Riker speak of the ship as a prestige posting, for elite officers only, & some others echo that sentiment, but I've never seen any of that position from Picard. He's almost a refuge for misfits.