If you mean a random mediocre white wine and a random mediocre red wine... sure. Blanc de Noir is a thing and there are some high acid low tannin reds with minimal fruit and some minerality... I'm sure I could be fooled, they're not expensive, though.

If you mean a dyed (red) white whine versus a fruity Pinot, a peppery Syrah, or a leathery Cabernet... not so much. Varietal and the procedures that go into expressing them (oak, tannins) are so different that people with a nose would notice. The same is true in reverse of a buttery oaked Chardonnay that nobody bothers making as a red wine. That's completely ignoring the unique honey flavor of late harvest Butrytus that is unique to Sauternes and some Riesling, which you will never find in a red.

Similarly, the taste of age (oxidation) is fairly unique so you would notice the difference between a 3 year old and a 13 year old properly stored wine, unless someone went to amazing lengths (there's money in those hills!).