There's is a maximum number of 100 items the exploring dweller can hold. So is there any indication when the character hits 100 items?
Unfortunately not. To get the exact count, the only way to do it is by counting.
However, as loot drops approximately every hour, and the events like the NGD also have a chance of dropping items, a dweller will typically reach 100 items around 90-95 hours. So just recall the dweller around that time.