Okay, I need to admit that I did it for science. I already had 200 tier 1 dust (maximum) and was able to collect 50 more from the objective. I was just like “come on give it a shot and lets see what happens”.
Guess what? Dust goes in overflow:

I did the same with glory but it caps out at 15k and nothing goes in the overflow.
The reason behind is probably that glory is a currency and dust is a resource but perhaps the max. Cap of Glory (15k) can be extended soon? Incursion currency was extended, loyalty has no max, BC has no max.
Would you also like to see the increase of the glory cap?