Current state: yes and no. 

You can set specific permissions on custom pages, so you could create a role-based custom page and make it only visible to the certain role. 

The tricky part comes in changing the default landing page when they log in. I’m not sure if that’d be possible. 

Future state: 

Depends on your use case. I believe the road map has plans to add permissions to widgets, so that you could customize the home page for different roles. That’s a different, and perhaps more complicated, use case, but it’s similar in customizing the home page to specific roles. 

Custom pages for specific roles is squarely in the use cases for custom pages, so that’s probably a simpler fit. Not sure if there’s anything in the road map for altering the default landing page upon log-in, but I think it’s directionally in line with product vision they’ve shared. (My two cents is that it’s a bit too niche and complicated to expect this as an out-of-the-box feature any time in the next year. But you could always look into if it’s possible to do with a third party script or something else)