How do ionic, polar, hydrogen-bonding and non-polar compounds compare in TLC?
No, your analysis is wrong. 

The nice thing about TLC is that you can pick the "paper" and the solvent to suit your analysis. So if you use benzene as the solvent then it won't "drag" ionized compounds along behind the solvent front very well.  If you use water ionized compounds do get dragged along nicely.