If your modem only has an internal antenna, then I would expect that adding an antenna that is external to the modem will improve reception. But adding a random pigtail length will not yield predictable results.
The proper approach is to run coaxial cable from the modem to an antenna. The antenna could be a simple, small, vertical wire antenna that you would place on your dash or on the ledge/deck by the back window. The size of the antenna depends upon the carrier and country you are in. A 700 MHz antenna would be approximately 10 cm tall while a 2100 MHz antenna would be approximately 3.4 cm tall. If you could add details of your carrier name and country, a specific antenna design can be given.
A slightly better approach would be an external antenna. Getting the antenna outside of the metallic body of the car often greatly improves reception. Recognizing you don't want a shark fin or similar, a reasonable compromise antenna is one that simply sticks to the glass on the outside and there is a small box that sticks to the glass on the inside - no holes to drill. This type of antenna does not work well, however, near in-window defrosters or with metalized glass. But it is removable if you change your mind or you sell the car.
One other option is to simply relocate the modem to a location that is more favorable for reception. Placing the modem on the back window deck of the car may sufficiently improve reception. This may be worth testing with some temporary wiring before going the route of the external antenna.