If you meet system suitability, the column is suitable. End of story.
If you don't meet system suitability, the column is not suitable, regardless of whether it passed the manufacturer's spec or not. The column manufacturer's test may or may not respond to factors that are important for your analysis.
As a matter of personal opinion, I think that the only meaningful test for an incoming column is an abbreviated form of system suitability (I usually focus on the retention/resolution/efficiency part rather than repeatability).
If you have been experiencing a significant number of failed columns on startup (columns that looked OK on the manufacturer's test but failed your system suitability), then doing this incoming test is a good idea (better to get early warning that your new column is a dud!). If you have not had a bad column problem, then the extra effort is probably not cost-effective, and relying on the manufacturer's test would be just fine.