In short, yes. Its done all the time.
If the switches have SFP ports, I would use SFPs instead of fiber converters. If you only have copper ports available, then the fiber converters are your only real option.
Now, the fiber type and converters will dictate overall speed of the link. If the fiber is a 62.5 OM1 fiber, your probably not going to get anything over 100 MBPS. If its OM2 or OM3, then you can probably get GIG speeds. If you have single mode, then your blazing...