I don't see any dojo in any style doing what I'd call conditioning.
In my Kenshusei program, the first class every day is devoted to conditioning. Sometimes it is ukemi work, sometimes calisthenic-type. Since all the students this year have knee issues, the classes have to be very imaginative, but last year they went running, did lots of air squats, etc.
Since a lot of aikido at our (beginner) level is unlearning strength and learning center, I think traditional weight training would be counterproductive. However, I think the thing keeping more of the advanced students from more conditioning is (1) lack of training tools and (2) lack of time.