Did Holdsworth tour the None Too Soon album?

[Average Joe]

Or play the material or other standards live? Does any live recording or bootleg exist?

I really like his playing on that record and on that sort of material, but the overall feel of the band and record is a bit stiff. Probably because it wasn't recorded as a band. I would have loved to hear him with a live band

[GuyBoden]

Plenty of Allan Holdsworth info on this blog on the web:
None Too Soon (album) - Allan Holdsworth Information Center

I believe that Gordon Beck was the instigator for "None Too Soon".

"At that time, Gordon often came to me, we were frequenting each other fairly because they were both engaged in similar projects, and the speech fell on that record. We therefore decided to take advantage of the favorable moment. We therefore called Gary Willis and Kirk (Covington) and began to choose the material."

[GuyBoden]

Gordon Beck played piano with Allan Holdsworth in 'Jazz Fusion' type groups in the late 1970's and early 1980's.

(Very slow download and very, very 'sounds out there man'.) Live recording here:
Allan Holdsworth, Gordon Beck, Jeff Clyne, John Stevens - Conversation Piece (1991) [Fusion, Free Jazz]; FLAC - jazznblues.club

[James W]

Regarding Allan playing standards live, there is this:

.. though it is a fusiony take on it...

[German Sanchez]

Or play the material or other standards live? Does any live recording or bootleg exist?

I really like his playing on that record and on that sort of material, but the overall feel of the band and record is a bit stiff. Probably because it wasn't recorded as a band. I would have loved to hear him with a live band

No. Allan never did a tour for the album None Too Soon.
He also didn't tour in 1996 to promote the album or anything like that.
The album was recorded in October 1994, mixed in 1995 and 1996, and released in September 1996.
The original idea for this came from his friend Gordon Beck after he did a rendition of Michelle by The Beatles in 1993.
By the end of 1996, Allan had in mind to redirect his language and vocabulary in his improvisations, venturing into the territory of 16 Men of Tain, which was totally different from how he had been playing before.