It depends on how many costumes they wanted to add. More costumes does mean longer delays, but it would take quite a few costumes to add up to enough to be that much worse than before.It is unfortunate, since I would have loved to see DLC costumes for non-Miis; however, I've heard that would actually cause difficulties in loading and stuff (such as the delay with the character portrait appearing on the CSS when selecting an alternate costume).
This will be a factor in modding in extra costumes, as well as straight-up running out of memory and causing a crash, though thankfully there's a lot more leeway in that regard than there was in Smash for.
I crunched some numbers a while back and we should be able to add about a thousand extra costumes before instability ensues loading their portraits. Though of course, the delay at that point would be... very bad. The portraits really are the only bottleneck seeing as Smash is only loading the selected alts into the match itself. If not for that, we could give every character 247 extra costumes and not have to worry about anything... besides our SD card..
It would have been nice if portraits were dynamically loaded and unloaded instead of being loaded in at once. That would have caused some choppiness while scrolling through your costume options, but would have at least eliminated the delay for fighters at the back of the line.