I agree with Les -- it's called a recovery week for a reason, and working out while "recovering" may defeat the purpose
Also consider that a major principle that this system is built on is the muscle confusion concept, which all things considered is a tried and true principle and often goes by other names. That one week of downtime with no weights will not only give your muscles a chance to recover from the past three weeks, it will also lull them into a false sense of security. Since they'll be thinking that the hard work is over and it's time to relax, your first week of lifting in Phase 2 will really shock them back into action. Doing weights during your recovery week will reduce that effect and reduce your overall gains.
That's my guess at least
