Most of the questions on this site about staying on either side of a long-stay visa come from people who do not need a visa for short stays in the Schengen area (like US or Australian citizens for example). People who do need a visa, like Turkish citizens, have much less flexibility.
Your type D visa isn't controlled by the Schengen regulations and the time spent in Poland under the type D visa does not count towards the 90-days-in-any-180-day-period limit so staying up to 90 days elsewhere in the Schengen area before the start of your stay in Poland is perfectly fine from that point of view. The “clock” would simply stop when your time as a student in Poland begins and you would never exceed the maximum.
But you need to have the right to enter the Schengen area in the first place. As a Turkish citizen, this means that you need a visa. Your type D visa exempts you from this requirement and would also allow you to visit other Schengen countries, but only if it is already valid.
You don't necessarily need to enter Poland first or to go there immediately so, if your visa is already valid, you could in principle tour the Schengen area for some time before actually starting your studies. So if your visa's validity starts a few weeks before the beginning of the courses at your university, you could squeeze a vacation in-between. But you cannot avail yourself of your type D visa before its first day of validity.
Theoretically, you could also apply for a Schengen visa to cover your vacation. It's perfectly legit and having a long-stay visa starting right after the end of the short stay should in fact help you a bit (as you are not at risk of staying illegally since you already have a title to stay fully legally in the Schengen area and should not need to convince the consulate that you will return to Turkey) but it means starting another application from scratch, with all the hassle, the fees, etc.
(Also pay attention to the formalities required by your student visa, some countries require long-stay visa holders to undergo a medical exam or registration with the local authorities within a certain time of entering the Schengen area.)