Yes. He was one of the best studio musicians at the time, and the record label didn't have confidence in Townsend's musical ability, so they called in Jimmy the studio musician, just to be safe. This was a typical practice at the time.
There is also a story that Jimmy Page wouldn't let Pete borrow his effects pedal (one of the the few in London at the time), so they relented by letting him play the solo. I think the first version is more realistic, although it may be true that Page did have one of the few effects pedals in London at the time. It could be possible that Page already was called in to play the solo, as he had for many other bands, and Pete could have argued "Let me try that pedal. I bet I could play something just as good with it".
But regardless of what actually went on in the studio, playing the solo on I can't explain is one of Pages documented jobs.
danelectro dc 59
She's A Lady. Written by Paul Anka, performed by Tom Jones, guitar by Jimmy Page.
The song "Here Comes the Night" by Them, dating from 1964 featured guitar played by Jimmy Page, whose tenure with Led Zeppelin began in 1968.
Led Zeppelin's guitar player is Jimmy Page.
Jimmy Page - Led Zeppelin
Jimmy Page
Jimmy Page
Guitar
martin guitars
danelectro dc 59
She's A Lady. Written by Paul Anka, performed by Tom Jones, guitar by Jimmy Page.
The song "Here Comes the Night" by Them, dating from 1964 featured guitar played by Jimmy Page, whose tenure with Led Zeppelin began in 1968.
Led Zeppelin's guitar player is Jimmy Page.
Jimmy Page - Led Zeppelin
a guitar
Jimmy Page
Led Zeppelin were Jimmy Page, John Paul Jones, Robert Plant, and John Bonham, with the aid of Peter Grant and Richard Cole