No. The Founder Institute has a mix of full-time and part-time Founders in the program. Many businesses get started with part-time Founders until the company gains traction. Once a company gets off the ground and is properly capitalized through revenues or investment, Founders can expect to start working full-time.
On the other hand, we have data that suggests that Founders are much more successful the faster they quit their day jobs after Showcase & Network Initiation.