Short answer: no.
Longer answer: Are you an experienced person with public transport? Even on the metro I think that travel time estimate is very optimistic. The airport is enormous - it took me 20 solid minutes to walk from my arrival gate to passport control. Then you'll have to find someplace to stash your bag first (you will not want to carry it with you) and then purchase tickets and navigate the metro with multiple changes (potentially including bus, which will be subject to the very bad city traffic). If you arrive during rush hour the metro is going to be packed. Then reverse the process back to airport, fetch bag, go back through security, catch your next flight. I don't have experience there, but the advice I read was at least 2-3 hours ahead of your flight time. And by the way I believe you'll need to buy a $50 e-visa to enter the country even for a few hours, but you will have to check on that.
IMHO that does not give you enough time to remotely do Istanbul justice. If you're there midday or on a weekend, all the tourist areas are very busy. The suggested Hagia Sophia is amazing, but it is a mosque that closes 5 times a day for prayers, and once it opens there is usually a pretty long line to get in, you would likely miss out just due to timing. Same with Blue Mosque. Other interesting sights require much more time and tickets (Topkapi palace, museums, cisterns, etc.)
Your available time pretty much gets you at least 3+ hours on public transit and not much looking at interesting things. If you're up for that, go for it. As someone else suggested, if you're on Turkish airlines you might be able to extend the layover for 12-24 hours.