Let me first start with the fact that I think flying without a visual reference is about the coolest thing in the world. One of the things that makes flying so cool: not only can you move in three directions, you can do it without seeing where you're going and still get home! Try that in a car (hyperbole, I know).
All that's to say when I started to plan on getting my ticket, the instrument rating was as as I could after.
Fast forward today, for various reasons I had to take a break from my initial private training. I'm due to start back up in the spring. This time I have budgeted six lessons (with instructor) a month. Not quite the 8 recommended (twice a week), but, enough that I could keep going as long as, I dunno, I don't lose my job or the mob finally finds me and makes me pay them back.
So here's the question. Can you train for both at the same time? I know I could set up my private cross countries to work towards the 50 for the IR, the 40 sim/actual time, sure..no prob.
I guess the follow up, is: is it smart to do so?
Lastly, if you were going to attempt this, how would you ask your CFI to train you? Similarly: If you wouldn't attempt this, what would you ask your CFI to do to prep you for it (e.g. maybe train to the IFR PTS standards, not the Private?).