Well, the question is rather naїvely phrased – could women ‘catch’ the TDF men? - but is worth discussion given the simplistic assumptions made by some commentators about how women compare with men in cycling performance.
Yes, some women could, given the right circumstances, but the question is a bit meaningless without understanding how cycle racing works and elaborating on context, or indeed clarifying better what is meant by ‘catch’.
Tour stages are ridden at varying levels of intensity (varying between days, within individual stages, between types of terrain, between rider roles and between breaks/peloton/autobus/stragglers).
So, there is no chance of any woman ever being able to ‘catch’ or stay for long with the men when the intensity is high - even Marianne Vos would find it impossible to stay with the vast majority of the male Tour riders in these situations, such as:
- riding a col, or probably any significant climb, hard
- battling crosswinds in hard-riding echelons
- in any break
- on the front
- time-trials
- descents ridden hard
- on cobbles
- fighting to rejoin if dropped
However, the top women on top form could probably ‘catch’ or at least stay with some of the TDF men in certain circumstances, such as:
- riding with the autobus on a col (a fresh Vos might even be able to go faster given her good power/weight ratio, but bear in mind watts/kg is not the same as the ability to sustain power)
- while remaining sheltered in the peloton (until the intensity got high, e.g. towards the end of a stage or on a strategic climb)
- beating the very slowest riders in a time-trial (e.g. those saving energy and simply riding fast enough not to get eliminated on time)
- maybe beating a heavy non-climber on a long climb (although note that the TDF sprinters can ride the big climbs pretty damned fast if they put their minds to it)
When I was riding Elite/1/2/3, Cat 2/3 and Cat 3/4 races in the 1990s, some of the fastest UK women (including national champions) sometimes entered some of the shorter Cat 3/4 races that I rode. In my experience, they never featured in breaks, never rode at the front, and never animated the race, but would often finish with the main field in less hilly races. There is a considerable gulf between Cat 3/4 races and the TDF and, whilst the recent advent of a developed professional female class has no doubt improved standards since then, this sort of evidence gives an idea of the gap needing to be closed in order to ‘catch’ the TDF men.
So, in answering the ‘catch’ question, one has to at least look at how women would fare if trying to ride at TDF speeds in TDF situations. Therefore, unless the OP is just querying the relative physiological capabilities of men and women in cycling, and whether these could converge at all (in which case why not pose a better question about comparative physiological data/research?), one has to conclude that yes the faster women could possibly ‘catch’ the slowest TDF men in certain circumstances or stay with the race in periods of low intensity, but they would have no chance of actually being competitive in any aspect of the race, or holding a similar length women-only race at similar speeds over similar terrain and distances.
That said, I doubt that it’s impossible that some women could ‘catch’ TDF men in other ways – such as earnings, fame – e.g. if women’s cycling became as popular to watch as men’s (as in tennis).