Affiliate Marketing Secrets

On Wednesday, I received a job offer from a law firm that practices exactly the niche area of law I’m interested in so I was very excited about the offer – they wanted me to start next week. I called them back yesterday to discuss the details of the offer and to accept the offer. I was informed that they would like to move the start date back a few weeks to late-January/early-February but they didn’t have an exact date at this time. I accepted the offer under those terms and asked that they send me written confirmation of everything we discussed with the precise start date. Should I wait until I receive their letter prior to sending my letter/email essentially providing written confirmation of my acceptance of the offer?