Yes, with practice, your pet will be fully capable of urinating and defecating while in the cart.
Some pets will take time to get used to the feeling of eliminating while in the cart, but most will catch on in a few sessions.
However, while your pet is in the process of learning this new technique, we do recommend that you make sure they are eliminating sufficiently by taking them out of the cart to eliminate if they have not gone within a reasonable amount of time.
We find it is helpful to take them out to the same spot in the yard each time so they learn to associate the trip with elimination. Using their “favorite” area helps by stimulating their sense of smell.

Wirey.