I don't think it would work with an undermount sink, but it should be doable with a self rimming style. If you have cabinets on both sides of the sink base, you can cut down the side panels of the base a few inches to give you additional width to install the sink.
Precision in cutting the opening in the countertop becomes more critical. (Your 33" base has only about a 32", or less, inside dimension.) I installed the counter, marked the opening location, then removed the countertop to cut the opening.
As mine was a stainless steel sink, I used plenty of caulk under the lip of the sink since I was not able to access the mounting clips. I then put weights in the sink until the caulk cured to get it to sit uniformly onto the counter.

I don't know if you are able to do this, but Elkay (and others)makes a number of smaller undermount sinks sized to be used as a double sink set up.