Honestly, I wouldn't recommend it. It does depend on what you really mean by "music production"... but if you're planning to use any current software or plug ins, you're not going to have a great experience with a Core 2 Duo these days. Even with more RAM, the CPU is going to struggle to keep up. Comes down to what kind of production you want to do. If you're a singer-songwriter type, and you just want essentially a modern version of a multitrack tape recorder to lay down audio recordings of vocals, guitar and whatnot, along with some light programming (drums, some synth etc) then it could be OK at a pinch. But if you're looking to make electronic music, then the computer itself becomes far more important as it's going to be the primary instrument and source of sounds in the first place. That means you'll want to be playing with lots of synths and effects - and you will very quickly hit a wall with a machine like that. Same goes for making film music or music using large orchestral sound libraries and that kind of thing.
IMO, it comes down to two basic choices:
If you're after a simple multitrack recorder in computer form, with only light use of effects, synths and processing, then you can get away with a lightweight machine (including older ones). In that case, you're better off putting some money into a good quality audio interface to ensure that what you capture is as nice sounding as your budget allows. But be careful when investing in a decent interface - if you spend a lot on something you want to keep for a while, you want to make sure it has the right connectivity that will still work on a newer machine if and when you get one. As in, be aware that firewire might not be the best choice moving forward...
If however you're looking to avail yourself of all the current software toys that everyone uses in proper "in the box production" nowadays (for electronic music, pop production, film scoring etc etc) then you need a machine that won't punish you for trying. A Core 2 Duo will probably struggle to manage even one instance of Omnisphere, and there are quite a few software synths that I doubt it could manage to run at all such as the (great sounding) uHE Diva. You'll end up freezing tracks all the time on an old machine and probably cursing a lot too. For this kind of production (for me personally) I'd only want a minimum of a quad core MBP. Doesn't need to be a current one, any of the 15 inch models from 2011 onwards are a quantum leap above the dual cores and are very well suited to music production. Short of that, I've seen some people using recent 13" MBPs (which aren't true quad cores but can do 4 thread with hyper threading AFAIK) and they aren't too bad. In my experience though, when you're running a lot of real time synths, samplers and effects, a minimum of 4 actual cores (especially hyper threading ones) is the baseline sweet spot. The faster the clock speeds the better, but in reality there's a massive jump in power and usability for music production between any Dual Core Mac and any Quad Core one. So if you've got a 15" i7 MBP quad in any form, it's going to be a good start, even the lower specced ones. The next thing is RAM, and I would recommend a minimum of 16GB today. 32 if you want to use a lot of big sampler libraries.
End of the day, any model of 15" quad core MBP (from 2011 onwards) would be the wisest choice if you want to not be frustrated by being careful of what you can or can't use. With a machine like that, even using just the internal drive for audio and a simple audio interface can cut it to do pro-level work. With something older or way lower specced, you'll be trying every trick in the book (fast external drives, squeezing in as much RAM as you can etc) just to get something passable, I wouldn't want to go that way. Hope this helps!
