You would definitely hear an improvement from replacing the factory speakers with higher quality ones. The factory speakers are almost certainly in poor condition after 34 years. You would notice an even bigger improvement if you added an amplifier. However in an '88 standard cab all the speakers are little 4"x6"s, which you'll never get any real bass from no matter how nice they are or how much power you throw at them. You could add a subwoofer or put a set of 6.5" round speakers in kick panels if you want more bass, either of these will require an amp as well.
The main benefits of the RetroSound Santa Cruz (or most any new aftermarket head unit for that matter) compared to the factory head units in these trucks are pre-outs for running signal to external amplifiers, sound tuning/crossover settings, and creature comforts like Bluetooth and AUX inputs. The Santa Cruz's internal amplifier only puts out 18W per channel RMS, so it's not really any more powerful than your factory head unit. You can hook external amplifiers up to it easily though, where as your factory head unit would require an external processor or an amp with hi-level inputs to do so.
A lot of this really depends on what you're looking for and how much time/money you're willing to invest.