Tung and linseed oil are considered "drying" oils that do eventually polymerize. As noted, mineral oil does not form a film. If you apply too much tung or linseed oil, they can stay oily or sticky for quite a long time. 'Polymerized' tung oil or 'boiled' linseed oil will dry and build a film much more quickly than the raw oils, FWIW.

: Can't imagine it why it would be any worse than tung or linseed oil.