It is possible for TS to run on a system with just CPU integrated graphics though walk might be a better expression. Generally almost any GPU will be an improvement. I used to run TS on a Windows 7 vintage laptop with a fairly basic Radeon GPU and found it perfectly playable with some of the graphics features turned down or off. Your card may not be new but TS itself is a pretty old program- as fabdiva notes though newer routes are much more demanding than those from even a few years ago. One thing you might keep in mind is that current editions of TS come with new (more demanding) routes so you might want to start with an older edition of TS. They can be found sold as Steam keys by third party resellers. On the down side refunds may be more of an issue than for items bought through Steam but they're often going for pocket money prices and, because they install through Steam, you'll still get the most up to date version of the core program so you needn't worry about backwards compatibility if you do go on to buy newer DLC.
