Yes, like
@Tophat1900 I find that exercise in the mornings, on an empty stomach just drives my blood glucose up and up.
Exercise later in the day then lowers my blood glucose.
There seems to be a lot of variation between people about how exercise affects them. And the type of exercise makes a huge difference. The intensity and duration cause different effects.
For instance, for me, a dog walk at lunchtime, medium pace, will reliably and comfortably drop my bg by 1mmol/l for an hour or two.
A run to the bus on the way to work will raise my bg by 3-5mmol and keep it up for hours (stress, physical exertion, glucose produced to deal with the stress... )
A strenuous hill walk will drop my bg like a stone (but not cause a hypo), and keep it low until I next eat carbs.
All of those happen to me when I am on a very low carb diet, definitely fat adapted, probably in keto.
All would have different reactions if I was running on carbs.
So really... you need to test for yourself, since I can pretty much guarantee that your reactions to those things will be different from mine!
Re HIIT: It is regularly recommended for type 2 diabetics as a superb way to build muscle and reduce insulin resistance. If you are interested in it, I suggest you test your blood glucose extensively to find out your personal reaction, and then choose a time, or a snack, that allows you to enjoy it, and the benefits.