"during DI" is the sticking point here. I can point you to numerous references1,2,3 that argue that constructors should not do "real work" (and others4,5 that argue that it's fine). That is, they should stick to validation and initializing state. But "during DI" can be taken to mean more than simply stuff constructors do. It's also the work done to call those constructors.
I know of no advice prohibiting network communication prior to calling constructors. Just understand, much like file IO, this will be slow.
Doing this work prior to construction means your dependent object will be ready to go whenever it exists. Thus you never have to ask it if it is. And you can be fairly confident that it's construction will succeed.
You can ignore all that I'm sure. Just keep in mind anything that the constructor does or calls is being shoved down the class users / testers throat. Be sure you mean to do that before you do that.
But it's not the same issue just because you're doing it "during DI". Unless you have some flaky DI framework that makes doing this work outside of your constructors a pain.