And a management tool won't make a bad manager better, they'll manage just as badly through the tool. It can actually make things worse if you're the manager of a bunch of managers who all use the tool differently: your reports from the tool will be meaningless at best. That's why my preferred approach is to add project management to a workflow tool; not the other way around (e.g. we don't make development leads enter their tasks into MS Project, we put the project tracking info in Jira and manage it through there.) That way you can drive data consistency through process consistency and not piss off your developers by wasting time with multiple systems.
Of note just because they use a pm tool, if they like keeping things close to their chest you can end up with a drip feed affect, with them only adding things to the tool when they think you are ready for new work.
This can then cause issues where the work they released needs further requirements capture....
But, as you say, if he was a good manager, he would be communicating anyways.
If the management is not so good (or just not good at communicating?), I'd rather have a good management tool :)