The short answer to your question is, "it depends." It depends on the source of collagen you are using, whether or not it is native or denatured, what the solvent is you are using, and what kind of printer you are going to use. Yes, you can print collagen only without any crosslinkers, but the application of your printed material will be relevant to whether or not you need to protect the scaffold from rapid degradation. If you are using cells in your application, you will need to have some kind of crosslinking mechanism to keep the structure intact. Uncrosslinked collagen does not maintain structural integrity in physiological conditions, especially if you have cells present. Are you willing to use non-chemical crosslinking techniques like dehydrothermal treatment, or UV irradiation?
You can increase the concentration of collagen to achieve the right viscosity (which is dependent on what kind of printer you are planning to use), but in concentrations of collagen above 10 mg/ml, cells will not penetrate the structure very well. I have managed to print some gelatin-only scaffolds in the past, but in vitro and in vivo the cells break down the structure quite quickly and you'll lose integrity of the scaffold you printed faster than the cells can reform their own scaffolds.
Hope this helps. Feel free to message me if you have any other questions.