Can both line and load go to same screw on a GFCI outlet?
You may be using the terms incorrectly.  "Line" and "Load" have special meaning with GFCIs, so I recommend not using the terms anywhere else. (well, smart switches it's OK). 

When you're dealing with ordinary receptacles, I recommend using 


Supply - the cable that is powered 
Onward - the cable that takes power onward to feed other loads


And do the same with GFCIs - don't call onward "load" or it gets too confusing.  

On a GFCI, "LOAD" actually means the GFCI will protect onward outlets if they are attached here.  That's a money-saver if you really want to do that, otherwise it just creates a big mess. You get nuisance trips from things that don't need to be on GFCI (lights) or that shouldn't be on GFCI (refrigerators) or people can't find the reset because it never occurs to them it's GFCI. 

So if you really want to GFCI-protect onward wiring, attach it to LOAD.  Otherwise, leave the warning tape on there and attach the onward wiring to LINE. Please. 

Most GFCIs these days support 2 wires on each LINE screw, using screw-to-clamp methods.  Screw down quite hard, actually use your torque screwdriver to spec.  Or pigtail.  Avoid "Back stabs" for reasons often discussed here.