Crystallization in the column is also possible and especially, if the solute crystallizes in the eluent solvent at temperatures that are little lower than room temperature.
On the other hand and concerning the intermolecular H-bonding in the column, I don’t see the “why not?” because fluorine group is H-bond acceptor and dichloromethane is H-bond donor. Besides, the presence of a non-polar solvent like pentane, favors the intermolecular H-bonding:
How good is fluorine as a hydrogen bond acceptor?, Tetrahedron, 52(38), 12613-12622, (1996)
https://www.sciencedirect.com/science/article/pii/0040402096007491Fluorine as a Hydrogen‐Bond Acceptor: Experimental Evidence and Computational Calculations, Chemistry, 20(35), 11058-11068, (2014)
https://onlinelibrary.wiley.com/doi/abs/10.1002/chem.201402858Weak Intermolecular Hydrogen Bonds with Fluorine: Detection and Implications for Enzymatic/Chemical Reactions, Chemical Properties, and Ligand/Protein Fluorine NMR Screening, Chemistry, 22(22), 7592-7601, (2016)
https://www.ncbi.nlm.nih.gov/pubmed/27112430IR study on double hydrogen bonding in dichloromethane, Journal of Molecular Structure, 275, 203-210, (1992)
https://www.sciencedirect.com/science/article/abs/pii/002228609280195NRole of chloroform and dichloromethane solvent molecules in crystal packing: an interaction propensity study, Acta Crystallographica B, B69, 379-388, (2013)
http://scripts.iucr.org/cgi-bin/paper?S2052519213015078