Not really - map rank doesn't take into account what it would be like if you only played 1v1's. It merely takes into account the points you've gained in lost. For example, let's say you never played a 1v1 until your score was 1600. Then you played 100 1v1's, all vs another player exactly with the same score of 1600, and you won equal 50-50 in an alternating fashion (you won one, then he won one), etc. Assuming you gained 20 points then lost 20 points each time (although it might be slightly off, bear with me), you'd have broken even at the end.
Thus you'd be still at rank 1000, being whatever that is, a private I believe, even though your competition was rank 1600. It's the same with someone else who could be a cook, if they only played another cook the same rank and started playing that gametype when they were a cook.
EDIT: ffs you edited your post it looks like I'm responding to nothing
