Is a transit agreement with a tier 1 provider sufficient to connect to the entire internet? Suppose I'm a Tier 3 provider with my own autonomous system number and ip address range, who purchases a transit agreement with a single Tier 1 provider. Is this agreement sufficient to send and receive data from all other users connected to the internet? Or are further agreements with providers further downstream again required?

Yes. In fact an agreement with any tier provider is sufficient. The difference is reliability, bandwidth, and cost.