That's exactly how I would think of them, yes, but depending on the progression, the numbers may or may not be degrees of the original key.

For example, Desafinado is in the key of F, so when I think of the melody, it's like 5-6-7-1-7-6-b6-6-1-b6-b6. The bridge, though, does like a I-VI-II-V motif in A, then again in C, so when I'm playing the melody there I'm thinking in terms of those keys. The first thing in A would go something like this: 3-4-5-6-5-4-3-4-5-2-2 (in the key of A); then change key when it goes to C.

A little convoluted, and maybe not for everyone, but that's just the way my brain's been working for a long time, and probably will never change, lol.