Assuming a star in such a cluster could have planets, would they be so irradiated as to prevent life?
I think the star the planet orbited would dominate the cosmic irradiation, but I don’t know for sure. A good question.
The greatest danger would be orbital instabilities caused by stars being so tightly packed together. Near the core stars are even colliding and merging when normally that is extremely rare in our region of the galaxy. A star system on the outer reaches of a globular cluster might be safe for a while, but even the orbits of stars around them tend to be erratic and very elliptical, sporadically carrying them in and out of the central regions. I doubt life on any of them could survive for very long.