Yes, but you could have an extra 15 hours or so in Madrid with the time you'd save. In fact, you'd have an extra 30 hours by the time you've counted the return trip too. You'd still be with the same people, you've still got your cans (or more likely pints/bottles in a bar), so it comes down to a simple choice - over a day spent in Madrid or on a train. Know which one I'd choose.
And from what I remember, having looked into the option of a train from Madrid to Paris as an alternative to flying when I was hard-up, I expect the train would work out a fair bit more expensive. I'm pretty sure the train wasn't all that cheap, and by the time you add in your travel down to London and the Eurostar to Paris, I'd say flying would be a fair bit cheaper. Not 100% sure of that, mind, but I suspect it would be.
All hypothetical, of course, as you've not even drawn Madrid yet
