No, and that access does not exist regardless of who deposited the money or how much was sent.
Inmates retain privacy rights over their financial transactions inside the facility. The account belongs to them, and the spending history is not visible to outside parties, including spouses and family members who funded the account. There is no portal, no statement, and no way to pull up a transaction log from the outside.
That said, it is worth putting your mind at ease about what the money is actually being spent on. The commissary is not a mysterious place. It is essentially a small convenience store stocked with items you would find at any grocery or drug store, marked up slightly because of the captive market. Tuna packets, ramen, chips, cookies, hygiene items, socks, shorts, maybe a pair of sneakers if they have been saving up. That is the commissary. There is no exotic category of purchase hiding in there that would change how you feel about sending money.
A hundred dollars is a solid amount. It gives him some food options beyond what the facility serves, which matters more than most people on the outside realize. Commissary food is not a luxury, it is how inmates supplement meals that are nutritionally adequate but not exactly satisfying. Knowing the money went toward making his daily life a little more bearable is probably the most accurate picture of where it ended up.
If you want to know how he is spending it, the most direct route is to ask him. Most inmates are happy to talk commissary.