Neither the IMEI nor the IMSI is used for authentication. The IMSI is slightly closer to the truth (while still missing by a mile), but without the per-IMSI authentication key (which is never transmitted over the air interface, whether in plaintext or encrypted), it's useless as well.
SIMs and SIM burners can be purchased trivially on the open market, and cloned without too much difficulty. Although, a social engineering attack on the employee at the cellphone store is a superior method since it automatically gives you a "known good" SIM with the operator's keys, etc.