A pilot who is current, rated and has significant experience on a useful type may have his or her CV kept on file at some companies. Many, however, now use online application forms which are often tied to a specific recruiting drive. Once the required number of new hires has been found, it's quite likely that all unsuccessful applications are ditched (data protection comes into this, but I'm not certain of the full ramifications) and no records kept.
There are some companies where CVs are kept on file, but that practice is decreasing as it is a fairly inefficient way of finding new people. It's much easier to get people to contact you than it is chasing around hoping old contact details are still valid. After all, there are more pilots than jobs, even now (and especially at your level); why keep redundant paper? One ad on Pprune, or in Flight, and companies are inundated with current, rated applicants. It's a no-brainer really!
So, yes: luck is still needed for those who have a TR and few hours.
Scroggs