GSM dongle instead of GSM shield?
Not directly. The standard Arduino Uno doesn't have the hardware/software necessary to act as a USB host, which means it can't talk directly to other USB devices.

You might be able to get it work via a USB Host Shield. I don't know how compatible that is with GSM dongles though because I assume you can't install drivers on it. Additionally, if you're using a shield anyway, you might as well use a GSM shield.

If you're able to get an alternative board then another possibility might be the Arduino Yún. It has a USB host built-in which is operated by the Linux part of the board. I don't know for certain that it would handle a GSM dongle, but it may be worth looking into.