If a meter meets its CAT ratings correctly under the current rules, then probably there is no problem. It is a little complicated however. Some meters are still being sold under the old CAT rating rules and as such they have slightly different and lower requirements.
A CAT rating is mainly for the protection of the user, not the meter. So if your meter is rated at CATII/600V right now it is supposed to be able to take 600V on any jack with any function without causing harm to the user. This does not guarantee the proper function of the meter above this voltage. Some meters have the proper safety ratings but also have a maximum voltage for a specific function. Any meter that claims 600V should take this on the AC ranges and the DC ranges without harm to the meter. A meter might specify less voltage for the proper function of the meter on Hz for example. If you apply 600V to a meter on its HZ range and it is only rated for 30V then it might not survive on that function and not indicate any correct readings on Hz anymore.
There is a clause though that appears to say that, regardless of the failure in any other mode, voltage modes must survive the torture test used for the specific CAT rating the meter has and it must still show the correct voltage so as to indicate the presence of dangerous voltages.
So the short answer is no. Measuring a voltage within the spec of a meter in AC or DC whether that is the actual type of current will not harm your meter. How else would you know if you have DC or AC sometimes? The long answer is it can depend on the meter and the function selected, ie: AC mV vs DC V, or according to what the manual says for that specific model. If it is a $5 meter then all bets are off. If it is a Fluke 87V then do almost anything you want on any range within the voltage rating of the meter.
Oh yes, some things to read on the subject of meter safety:
https://www.eevblog.com/forum/testgear/a-list-of-multimeters-that-do-not-appear-to-meet-their-claimed-safety-specs/and
https://www.eevblog.com/forum/projects/cat-ratings-and-interpretation/but if you are using the Fluke 179 then the really short answer is yes, use it on DC or AC to check any voltage or type of current flow up to its highest voltage rating without worry.