In my experience, to date, the answer is no. Again, this is my experience only. I will use the Rakshasa as a point of reference. A primary "defensive" advantage of the Rakshasa is the immunity to spells, thus giving it the CR of 13. But in terms of damage output and HPs, it is incredibly weak. That doesn't mean it is a terrible monster if played well by the DM, but it has a very different profile (consistency) than other CR13 monsters.
Once you get past the first 5 or so levels, the various abilities of the monsters, vis-a-vis the party, makes consistency a serious issue. Again, this is only my experience- others might have different experiences at their table.
I'll go with #lowkey13 on this. In planning my encounters for my party (run both at Levels 1-4 and now at Level 11+), two creatures with the same CR do not pose the same level of threat. Part of that I believe is due to PC abilities, but also part due to the (programmed) fuzziness of determining CR.
Let's face it; 5e is deliberately fuzzy on a lot of math and rulings. That's the Old School way. 4e was very consistent (as noted) and easy to predict, but 5e is not. Any DM looking for an A-B-C-D progression of how to design consistent encounters is going to be disappointed every time. Creativity and flexibility are the keywords for 5e.