of course
tab is just a way to organise visually your sketch.
you just  can't split method into several tabs.

It'll work

internally it's always one tab only

there is a class but you don't get an object  from it

Try this (no class here,.but 2 tabs)

1. // TAB1:
2. int x;
3. void setup()
4. {
5.   size(700,700);
6. }
7. void draw() {
8.   
9.   background(0);
10.   checkMouse();
11.   ellipse(x,100,100,100);
12.   
13. }
14. //TAB2:
15. void checkMouse()
16. {
17.   
18.   x = mouseX;
19. }

You're treating each tab like it's a different thing.