Nope. At a very minimum to hear SSB you need a BFO and results will be marginal.
To properly receive USB and LSB, the two modes of SSB, you need a product detector. There are many fine used radios that have that feature at low cost. Spend a bit more and you can buy new.
As I mentioned before, doing your homework is key. First, decide what kind of radio you want - in fact, since you're a ham, many HF transceivers these days have general coverage rx enabled. But if you're looking for something seperate, or don't have a HF transceiver yet, take a look at this article from our wiki (note: anything in blue is a link)
Excellent advice by ka3jjz.
Dont overlook the budget models by Tecsun and Degen they represent great value for money and there is always a keen secondhand market for them should you decide to sell and upgrade later on.