Replacing outlet with a GFCI outlet
Is the tab broken on the hot side? Garbage dispisal, so probably a kitchen.

If the breaker double-wide? If so, you probably have a multi-wire branch circuit - so if you join the two hots you may find that the breaker trips hard as soon as you turn it on. 

If you have a voltmeter, check the voltage between the two hot wires - it should either be 0 volts (they are the same phase) or 240 (they are opposite phase and it's a MWBC - pretty common in kitchens to meet the "two 20 amp circuits" rule.

If the tab is NOT broken and the voltage between the wires should then be 0, yes, you can splice and pigtail.