I don't know how a cordless phone will respond to the frequency change, but I can tell you that an AC-powered radio alarm clock goes a little nuts when switched from US (60 HZ) to Europe (50 Hz, also used in India).

It appears the clock uses the current's cycle to tell the time (marking the seconds as cycles of 60 peaks in the current) meaning that the clock runs about 17 percent slower when used in Europe.

I imagine that if your phone has an answering machine, it could wreak havoc with the timestamps on your messages. Maybe it would be a good idea to pick up a phone in Europe if you can. It's somewhat likely that you'll be transiting through a European hub on your way to India anyway, and many of the large airports have electronics stores on site. I know FRA and MUC do, and I thought I saw one at LHR as well when I was last there. I would imagine AMS or CDG and the like would also have something. Maybe even MXP...