While it is technically true that Prince and Sheila E. spent about a week on the album together, the reality is that almost all tracks were recorded weeks before Prince even considered the idea of conceiving a solo record for her.
Princevault's entry for the album explains its start:
Prince urged Sheila E. to record a solo album starting in February 1984, when she came to visit him at Sunset Sound during initial sessions for the Around The World In A Day album, following a friendship which had begun almost six years earlier.
Her album took shape right then:
"The Glamorous Life", "Next Time Wipe The Lipstick Off Your Collar", "The Belle Of St. Mark", "Shortberry Strawcake" and "Oliver's House" were initially intended for Apollonia 6 until Prince began to work with Sheila E. in February 1984, at which time he set the songs aside for her.
As you'll note, that's five of the six songs that make up her album, all of them recorded in weeks prior:
Sheila and Prince only collaborated on one track:
Noon Rendezvous is the only track on the album to have contained writing input from Sheila E. (despite the album's credits stating she had written all the songs)
Noon Rendezvous was recorded in mid-February 1984.
However, there was one possibly hectic week where they recorded her vocals and percussion for the album:
Sheila E.'s vocals and percussion for all tracks were recorded in the first few days of April 1984.
Astonishingly enough, it appears those recording sessions started out with Sheila E. recording her vocals for legendary Prince B-Side "Erotic City", though it seems no confirmation of this was obtained from others involved, hence Princevault saying:
It is possible that Sheila E. added her vocals sometime between 1-4 April 1984, when Prince and Sheila E. worked on tracks for her album The Glamorous Life, but this is uncertain.
An in-depth exploration of the recording of Sheila E.'s first album is part of Duane Tudahl's excellent book Prince and the Purple Rain Era Studio Sessions - 1983 and 1984. Apparently a first version of her album was compiled on 28 March 1984; however at that time the tracks did not yet feature her drums or vocals. The next days -- 29 March to 2 April -- were spent recording her contributions. (On 2 May Warner Bros. Records released "The Glamorous Life" as a single.)
It is somewhat disappointing that Sheila E. exaggerates the recording of her debut album, when its actual story is pretty remarkable by itself.