Answer by taking a quote from the following article:

Alexandra Elene MacLean Denny (6 January 1947 - 21 April 1978) was an English singer-songwriter who was lead singer of the British folk rock band Fairport Convention. She has been described as "the pre-eminent British folk rock singer". After briefly working with the Strawbs, Denny joined Fairport Convention in 1968, remaining with them until 1969. She formed the short-lived band Fotheringay in 1970, before focusing on a solo career.

Her nursing career proved short-lived. In the meantime she had secured a place on a foundation course at Kingston College of Art, which she took up in September 1965, becoming involved with the folk club on campus. Her contemporaries at the college included guitarist and future member of Pentangle, John Renbourn.  After her first public appearance at the Barge in Kingston upon Thames Denny started working the folk club circuit in the evenings with an American-influenced repertoire, including songs by Tom Paxton, together with traditional folk songs. Denny made the first of many appearances for the BBC at Cecil Sharp House on 2 December 1966 on the Folk Song Cellar programme where she accompanied herself on two traditional songs: "Fhir a Bhata" and "Green Grow the Laurels".  Her earliest professional recordings were made a few months later in mid-1967 for the Saga label, featuring traditional songs and covers of folk contemporaries including her boyfriend of this period, the American singer-songwriter Jackson C. Frank. They were released on the albums Alex Campbell and His Friends and Sandy and Johnny with Johnny Silvo. These songs were collected on the 1970 album It's Sandy Denny where the tracks from Sandy and Johnny had been re-recorded with more accomplished vocals and guitar playing. The complete Saga studio recordings were issued on the 2005 compilation Where The Time Goes.  By this time she had abandoned her studies at art college and was devoting herself full-time to music. While she was performing at The Troubadour folk club, a member of the Strawbs heard her, and in 1967, she was invited to join the band. She recorded one album with them in Denmark which was released belatedly in 1973 credited to Sandy Denny and the Strawbs: All Our Own Work. The album includes an early solo version of her best-known (and widely recorded) composition, "Who Knows Where the Time Goes?" A demo of that song found its way into the hands of American singer Judy Collins, who chose to cover it as the title track of an album of her own, released in November 1968, thus giving Denny international exposure as a songwriter before she had become widely known as a singer.

Did she agree to join?
She recorded one album with them in Denmark which was released belatedly in 1973 credited to Sandy Denny and the Strawbs: All Our Own Work.