Yes, if they have the time to do it.
Nothing in the move suggests otherwise:
When you have downtime (hours or days) and XP equal to (or greater than) your current level + 7, subtract your current level +7 from your XP, increase your level by 1, and choose a new advanced move from your class. If you are the wizard, you also get to add a new spell to your spellbook.
Choose one of your stats and increase it by 1 (this may change your modifier). Changing your Constitution increases your maximum and current HP. Ability scores can’t go higher than 18.
The only limitation is that the character has to be in downtime.
If in your game it is established that you need some hours to level up, you can do it twice in twice the time. For example the last time someone leveled up he did it during a quick rest of 2 hours, now for doing it twice you need
approximately 4 hours.
If this is the first level up is up to the players to decide how much time is needed.
EDIT: On the time issue
For leveling up you need current level + 7 XP and an undefined quantity of time (which may vary between hours or days).
This is supported by the fact you can't reach days of needed time by level + 7 (max 17) hours using the math suggested in the comment below, and there is nothing to say when to use hours and when to use days to level up.
The Make a Camp move supports the non-growing time requirement too, by letting you level up while resting in your camp. I don't think nobody would camp for up to 17 hours, or even between 8 to 17 days, for leveling up while traveling or even on a quest to save the world.
From my point of view (I may be way wrong, and if so you can explain to me where I'm wrong; please do so) The hours time restriction is there only to prevent leveling up mid-fight or in some other tense situation. Make camp, have some time to chill out and you'll gain your new skill. On the other hand, the days restriction comes to play when the table prefers leveling up off quest. Get back to town, throw your party and the next day start perfecting your skill.
To conclude (again, in my opinion) forcing a fixed time restriction for leveling up it seems to go against the principles of "Draw maps, leave blanks" which is at the core of the game.