See ... another poster says 'pretty straight forward' ... and that's true.
... but ...
Considering ... 'never updated' and experience with ... going to have trouble question could be answered both ways ... yes/no ... much depends on your experience and I'll be so bold as to say what platform (OS) and how it's hosted.
Can't go from 2.7 to latest 3.7 in one step ... must marched through versions ... and at each step along the way backups - so you don't loose ground.
Then there is PHP/MySQL requirements for newer versions ... along the march you'll have to upgrade PHP/MySQL ... but not too far ahead of what moodle will run under.
The other route could also have catch 22's ... this route ... stand up a new 3.7.x, get it running, then restore backups of courses that contain user info/work, etc.
Number of courses?
Catch 22 - plugins used in the 2.7 may not exist in 3.7 - role conflicts if Admin level users also enrolled in courses. Example: in 2.7 old assignments mod were used in courses and never converted to new assignments mod.
Hosting ... hopefully not remotely hosted on a shared system.
Need full control over server to be able to upgrade PHP/MySQL at appropriate times.
Can it be done ... yes it can. If going the march route ... clone what you have to a test setup and test the march process there. Strongly advise using git for a march ... which would be the first 'major task' ... getting your cloned 2.7 site under git.
You have a lot of work ahead. Don't promise it will be done in 'short order' ... leave yourself plenty of 'wiggle room'!