No. Radiation effects are based on time and exposure level, and even with dust kicked up they're not likely to spend enough time there that it makes them sick at all.

Breathing in radioactive material from the dust is a bit more of a problem, but I'd expect they're wearing at least basic masks outdoors.

No radiation suits, though.

They'll carry some dust with them wherever they go, but like dust from anywhere else, it will slowly be dispersed on roads and in rain gutters. It's not "instant death dust" so while it will increase background radiation somewhat where it lands, unless someone eats or breathes a lot of it, they won't be affected.

So, still not a good thing, but not something that's a huge problem compared to flying bullets.

Now, if they punch a hole in the new safe confinement and a lot of water gets in, that will be much more of a problem.

The Chernobyl exclusion zone extends miles outside the reactor, and gets tourists. I think the danger level is more like "don't live here or you'll get cancer" than "don't walk here or you'll die". And don't pick up sketchy looking things because they might give you cancer. Inside/near the sarcophagus is a different story (that I don't know, but assume is much worse).

For example, the local wildlife is apparently doing better now than it was before the meltdown, because of lack of human activity. Not counting right next to the reactor where things died.

Hopefully the Russian troops don't interfere with ongoing cleanup efforts...

https://en.wikipedia.org/wiki/Chernobyl_Exclusion_Zone#Radio...