GIMP (gimp.org) is good but it's slow to load and not very responsive to pen controls. Also it is limited to 5 levels of pen pressure, whereas your wacom probably has 256 to 512 levels.
The slowness results in things like when you try to draw say, a circle, you end up with a series of lines instead of a smooth curve, because the code is not well-...
Take one big sheet of paper, of the size of each model of monitor you want to try, put some marks on the active area... And imagine they are the actual monitor. Make the kind of drawings you are used to do and define if YOU need it. ;o)
The only one that can answer if you need it is you.
To my knowledge, using the existing tools in Illustrator. All you can do is join the paths, then use the Width Tool to alter any portion of the paths after they are joined. Combining paths pretty much always resets any width markers.
However, if third-party plugins are an option, Dynamic Sketch from AstuteGraphics.com will allow you to continue paths as you ...
There's the width tool. With it you can make curves to have non-uniform widths.
If you combine with Ctrl+J 2 paths which both have have or another of them has width variations, the variations spread along the joined path. => The width tool is only a workaround which should be used after all needed paths are drawn.
Double click the Paintbrush tool. When the Paintbrush tool options appear, uncheck "Keep selected".
Then when you draw, the lines won't join up if the ends overlap.
Example: This is using a pressure sensitive Calligraphy brush to give variable stroke widths.