Is there a way to use a cell phone as a modem and then use a phone software like Classic PhoneTools to call another (cell) phone?
Yes, with most smartphones you can do something like this if it has been unlocked. You first need to tether the device to your computer. This is typically done through the use of an app which is installed on the phone and a USB cable. Now that you have your phone tethered, it acts like a gateway, you can run any program you want through it.
Keep in mind though that this may void your phones warranty, be against your terms of service, and it may also cost you a lot if you don't have a data plan.
If you don't mind calling from a different number, and are in the US, it might be much easier for you to use phone dialing within Gmail/Google Voice. If you sign up for a Google Voice account, you can place calls from Gmail using your computer's microphone. The number on the receiving phone will appear as your Google Voice number.