Does that idea seem to hold much water when we're talking about, for example, the fork reinforcements pictured in the OP...which feature all four 'suits' at once?

I have a pretty hard time imagining that an example of the symbols associated with all four suits, collected together (as on those reinforcements, or as associated with the Ciocc marque), lacks any connection to playing cards, on which those same four symbols have appeared in association with one another for centuries. Clearly there is a direct, intended reference to the suits on playing cards here.

If just one of these symbols in isolation - maybe, but still probably not. Colnago = club, Confente = spade...I'm already sensing a pattern, and that sense gets awfully strong once I get to Ciocc, etc.

There really does seem to be a pattern of use of these symbols in the bicycling world, and perhaps the most famous example, the Colnago 'cloverleaf', seems to have been referred to all along in Italian (by Ernesto Colnago, no less) as the ​asso di fiori...i.e. 'the ace of clubs', though 'fiori/fiore' means 'flower(s)' in Italian (plural/singular forms of the same word), and that latter association may have had a role in the symbol's selection for the logo also.

There are some stories about that, apparently, that offer differing accounts of the addition of the club symbol to the 'C' as Colnago's logo ca. 1970.

For some fragments from published accounts of the origin of the Colnago 'Ace of Clubs' logo, check out:

ITALIAN CYCLING JOURNAL: Unraveling the Mystery of the Colnago "Clubs"

I don't know if there's a bigger story here in terms some specific set of associations between the set of symbols associated with playing cards and cycling/racing more generally...but I'd be inclined to dismiss out of hand the contention that it's just a coincidence, and would love to hear more if folks have any insight into this question!