Sort of. The sustain portion of most instrument sounds has a relatively simple, regular waveform which can be manipulated to sound like another instrument. I wouldn't call this 'synthesis', that implies starting from nothing. Modification, transformation perhaps?
But a whole LOT of an instrument's character is contained in the attack portion of the note, often a much more complex, even chaotic waveform. This part of the sound is much more difficult to deconstruct and modify.
Some of the most useful sounds in our toolbox come from the 'hybrid synthesis' era, notably the Roland D-50 and the Yamaha SY range. A sampled attack was followed up by a synthesised sustain and release. The brief sample gave authenticity, the synthesised sustain was very controllable. Best of both worlds.