Definitely not, cos film SLR also can put on circular polariser what. If it's the same, then why bother with cross-processing?
In digital, the effect of cross-process can be imitated by adjust the contrast and the individual colour channels in Photoshop. However, the effects of cross-processing can be quite unpredictable on film, so it's really hard to imitate or even define how exactly a cross-processed picture should look like.
Cross processing is processing slide film in C41 negative developer and vise versa. For example when processing most slide film in C41 neg chemistry you wind up with really funky pastel colours though as has been noted earlier you can get unpredictable results.
From the look of your 2nd post I'd suggest your friend is either using an intensifier filter (didiyum etc) or a polarizer.