Never, unless you play indoor golf.
A true fitting can only be accomplished if you're doing it on the same conditions you will be playing on.

2 reasons to decide on an indoor facility for a fitting. Mats are not the same on turf interaction. Shot monitors add a lot of assumptions into launch, peak height, and descent angle based on 12 feet of ball travel.
Especially with wedges, it is difficult to be able to take the results outside and achieve the same response.
I’m a confirmed believer in an indoor SAM lab for a putter fitting. Takes out the variables not directly related to my stroke. After that, give me grass.

Agree with Don, outdoors is ideal but I will also add, if indoors is all that is available besides just buying a set off the rack, do the indoor fitting. You can at least get a good idea for basics like length, lie angle, shaft firmness.

I have my first official indoor fitting in 2 weeks with a Titleist rep. I played all winter on a Simulator, and I can say that the Trackman will under-estimate the distances that you will see on a real course. I assume all the other data is accurate.

I read an article on the Trackman website that said that they compared iron launch and spin numbers for a plus handicap hitting off grass versus a mat. This player launched the ball higher with less spin off the mat than the grass. The numbers were pretty significant, over 1* different in launch angle and near 500, maybe 1000 rpm of spin difference. Every artificial turf is going to be different but this was enough for me to opt for outdoor fittings. Driver might be the one exception where turf interaction isn't a concern. If using a Trackman with a RCT ball, the data is pretty good. I would argue it would be better than outdoors on a range with whatever beaten up range ball the course uses.