You can (almost) always
You can (almost) always fuse a piece of glass to itself. Not all glass holds up well at fusing temperatures though — dramatic color changes (including going from transparent to opaque) and devitrification (scum forming on the surface) are not uncommon.
I have seen streaky glasses come apart after fusing — that was likely caused by the COE of one or more colors in the streaky shifting away from the rest of the glass.
When in doubt, test 
Paul
FusedGlass.Org
Helios Kiln Glass Studio
PaulTarlow.com
