Hi jhwest69, welcome to the Forum.
Yes it is quite feasible to create an image of your 175gb C drive. In fact a back up image is essential if you have data that cannot be replaced.
I do a weekly image of my C drive which is about 42gb & using a USB 3 external hard drive, the image process takes just over 5 minutes, using Macrium Reflect.
There is no reason why it should not work as images are a very common method of backing up the system.