Can't answer for Alistair, but for me, yes
I can recite the numbers for songs I know.

This is how I learned early on. The interval method lets you play in any key .. and on any instrument. So playing a melody on trumpet is the same as on keyboards when you think of it this way, even if you need to play in C on trumpet and Bb on piano .. or Eb on a sax. Knowing the intervals makes it much easier than transposing in real time while thinking about which instrument you are holding.

My second trumpet teacher (think I was around 8 years old) used to make me play my practice piece in a new key at my lessons. On the spot. Once I caught on to the 'intervals' method it helped in a lot of ways. I stopped memorizing fingerings and started memorizing the piece!

As Mac mentioned; this expands as you begin hearing things in intervals, and then you'll recognize the notes for a given key. Even if you don't end up acquiring perfect pitch (like some lucky ones); as long as you know the key you know the notes you are after by their relationships. At least it seemed to work like that for me and others I have worked with.

I can't say I can hear a chord and tell you the exact notes out of the blue .. with no reference for key like some people can. But I can hear what they did in the key I'm thinking in.

In other words I know they went up a fourth, just not always sure if it was C->F or D ->G without knowing the key.

Long as I know the key I'm usually OK.
It should be a fun exercise for those who haven't tried it.

I do not work here, but the benefits are still awesome
Make your sound your own!