If you don't have G-sync or FreeSync, or vsync turned on, tearing is always present. Whether you notice it or whether it bugs you is a very personal question. Some people are more sensitive to it than others. It's like the Matrix - nobody can tell you if you will be sensitive to it. You have to experience it for yourself. So asking about it on a forum can't really enlighten you.
There are some very good TN panels out there. The best laptop display I've ever owned was a TN panel (about 95% Adobe RGB and nearly 2000:1 contrast ratio and an anti-reflective coating which made you forget it was glossy; the only better screen I've seen is OLED), and I do a lot of photo editing so color shift is a big deal to me. The problem is there are a lot of terrible TN panels out there too - some are so bad just looking at it straight the colors at the top will differ from the colors on the bottom. When you buy a VA or IPS monitor, you can expect it to meet some minimum level of image quality. When you buy a TN panel, you have no idea what you're going to get. It could be good or it could be terrible. Make sure you've seen it for yourself before buying, or reviews have vetted it as a decent before buying a TN panel.