Probably, though no guarantee.
If you can't buy the EXACT same module, then you should at least get one with the same amount of memory, frequency and same CAS (i.e. CAS9). If the CAS isn't the same you may have a timing mismatch issue. There are other timings as well but CAS is the most important.
To verify:
1. Click "XMP" in the BIOS (if Intel. Use Auto/AMP or whatever for AMD). Then Save settings.
2. run MEMTEST for a full pass to confirm it's working www.memtest.org
You will have to change the Boot Order in the BIOS so the DVD or USB (as appropriate) comes first or you won't boot into Memtest.
Other:
I'm not sure what "XMP" or AUTO will do when you have different modules. Possibly default to the lowest frequency (i.e. 1333MHz). This may even depend on the motherboard BIOS used. So there's a good chance you will have to MANUALLY change your settings (frequency, and possibly timings) to get the best results. Again, repeat Memtest any time you change settings.