Maybe. It depends on how Linux is set up. For a full panic, I'm guessing "no". There are a few facilities for collecting panics, from crash kernels to the netconsole feature. However, I don't know if any of them are enabled by default on your Linux distribution. I collect these panics by sending all kernel messages to a serial port, then collecting them on another computer. Supposedly, this can be done over USB serial as well.
For a non-panic oops, you might find something in the log files in /var/log.