No, "Slots" are the blocks where the name of the Unit appears.
If you have no free Slots, you can't hire troops of a kind that you do not already have (even if you are below your limit) - for example, if you have 4 slots and Marnid and Borcha with you, you could have only one unit type... I guess you have Watchmen, and you can only recruit townsmen&co atm?