Nope.
Beck stormed off stage and quit the group while they were on tour in Germany. Page quickly formed the 'New Yardbirds' to complete the tour and their contract. They disbanded after that.
Not exactly. Beck and Page were in the band together for a while. Clapton quit the Yardbirds after they had their first hit single because he thought they were becoming too commercial, not staying with their blues roots enough. They went to Page to ask him to join, but he had 6 months worth of studio work lined up and turned them down. He recommended Beck to them. When their bass player quit their original rhythm guitarist switched to bass, and Page joined along with Beck. Beck quit when after months of continuous touring they finally got paid, and it was a tiny amount of money with the record company taking almost all of it for expenses.