It is quite likely that it does contain them, yes.
A randomly chosen nonpaywalled study of Mediterannean tuna (DOI: 10.14411/fp.2014.011) says that
Overall, 84% of the gills examined harboured metazoan parasites.
Now these are the gills, not the meat in the tin, but it is unlikely that there will be much information on the meat itself:
The research on large tunas is hampered by the high value of fish; therefore, the studies on the use of parasites as tags consider mainly examination of gills, head and viscera, because of their limited (or null) commercial value
I don't know enough about fish parasite to tell you whether the 11 species found are all gill-only, but that sounds unlikely. Where there is an ecological niche, it will be filled. So, extrapolating from the gill parasite numbers to body parasite numbers doesn't sound too bad. And I am pretty certain that the people who prepare the fish don't have any method or reason to go remove the parasites from within the fish meat, just like apple sellers don't have a method to remove the worms from apples. So it sounds entirely believable that there are parasites in most cans of tuna, and if you eat enough of them, your chance of never eating a cooked parasite goes against zero.