Yes, it can be done. You would be amazed at what is made from glass fiber including helicopter transmission cases, leaf springs for heavy trucks, entire vehicle chassis, engine mounts, suspension mounts, crossmembers and driveshafts.
The drawback is cost and manufacturing complexity. Numerous successful composite projects have been canned due to cost and complexity despite passing structural and consistency testing.
Are you thinking of using prepreg or preform/injection?