You can definitely shoot the Milky Way with a 17-55 mm f/2.8 lens on a crop sensor. I've shot it with a 20mm 2.8 on a 7D and it came out just fine! So long as you set the lens to 17mm you should be fine.

To shoot stars, you can follow the rule of 600. Just remember to multiply the focal length by 1.6 to get the appropriate time. In your case, that would be 17 * 1.6 = 27.2mm equivalent focal length. 600 / 27.2 = 22 seconds exposure.

You can compensate by increasing the ISO. I suggest you take several shots with different settings to see what works best. I'd start with the lens set to 17mm and try a 22 second exposure at ISO 800. If it's too dark, you can increase the ISO. If the movement of the stars is too great (too streaky), you can decrease the time the shutter is open and compensate with a higher ISO.

Another option you have is to borrow or rent a different camera and/or lens. A 2 day rental would not cost very much. For example, this website has a Canon 14mm f/2.8 lens for less than $100 for 7 days. (I've never used this service, it's just an example.) You might be able to find similar deals on other sites.