No, it doesn't work like that. People typically set screen location hotkeys for each base, to jump back to base. I use F1-F6 for screen location hotkeys, moved all army to F7 and idle worker to F8 (so I can hit the right CTRL key with my thumb at the same time => select all idle workers = CTRL+F8). You can double tap control groups hotkeys to jump to that building/unit; but it becomes a problem if there is more than one unit and they are in different places. You can check out this example replay, where I practiced the terran 1rax FE opening; all the movements jumping around is done with double tapping control groups or screen location hotkey of the Command Center/Mineral Line area.

Btw can I select for example all Marines on the map without pressing F2 in case they're all spread out?

No, the only way to do it is F2, then CTRL click one of the marines in the middle bottom selection info panel. CTRL selects all of that unit (in this case your entire current selection), but normally it's only for the current screen without F2. On a side note, Shift is used to add/remove from your selection.