Does Paintshop Pro [any version] work with a touchscreen [monitor or laptop]?
Using the pen, can I draw, etc. on the screen in Paintshop Pro?
Regarding touchscreens, are you referring to a tablet/laptop/touchscreen running Windows 8, or some other platform? If the device and the version of Paintshop Pro both support the WinTab API then you should be in luck.
I, personally, don't like Windows 8, nor do I wish to promote it (it is just my personal bias), but Paintshop Pro x6 or 7 will work with the Windows 8 touchscreen. Quoting from PaintShop Pro X6: Best PC Photo Editor
The new OS matches smartphones and tablets not only with touchscreen operations but also with PC ultrabooks and convertible laptops which deliver better on board still cameras, light portability plus long-battery life for picture taking and picture processing on the go. But even more important to Corel PaintShop Pro X6 is the fact that Windows 8 supports the best set of touch screen operations and devices. Windows 8 supercharges painting and photo editing not just in PaintShop Pro X6 but most other applications.
You might also want to take a look at this question and answer: Are graphics tablets worth it?
As an aside, Paintshop Pro supports Wacom tablets and the associated "Wacom standard" protocol, and has done for a few years now. From Graphics Tablets: PaintShop Pro
In terms of 'bang for your buck', the current version of PaintShop Pro may be the best value on the market and it works perfectly with any one of the Wacom tablets...