Can I check shortened URLs?

Partially

Links shortened with a service like bit.ly are always redirects. So the broken link checker would always report them as redirects.  In the global configuration, you will find an option to ignore redirects for selected domains:  Domains to ignore redirects

The final destination is still reported as broken (HTTP Response code > 400). However, changes to the final destination (Redirects, HTTP codes 30x) or not reported.