This activity is ultimately underwritten by deposits.Yes and no. First of all, deposits are created whenever a bank gives out a loan. So it is not the deposit that makes loan creation possible, but rather the reverse: creation of loans is where money in deposits comes from in the first place. Without loans there would be no deposits.
Now the outstanding loans given by the bank are on the asset side of its balance sheet and there must be something corresponding on the liabilities side. For most banks, deposits are indeed a large part of liabilities.
However, the liability may just be a loan from the central bank or from other banks instead. It's not strictly necessary for banks to have deposits at all (and there are banks which specialize in such a way).
The only reason why it makes sense for banks to attract deposits is that they typically pay less interest on those deposits than they would have to pay for other refinancing options.
And again, all this doesn't say anything about the dynamics of the system, i.e. it doesn't say anything about loan creation. It's not like there is some process where the banks say "Look, we have X more deposits than loans, so let's give out some more loans". Some banks operate with more deposits than loans, others operate with less. In the end, they give loans whenever they find a creditworthy borrower.
In the overall system, i.e. when summing over all banks, the sum of loans is roughly the same as the sum of deposits, because loans are where deposits come from in the first place. (I say roughly because owners of deposits can transform them into other types of assets such as bonds.)