However, assuming both LOGARCHMETH1 and LOGARCHMETH2 are set off (which is presumably what the original poster meant), then after database restart DB2 will be using circular logging. Provided no transaction is so large/slow as to exhaust the primary and secondary logs then the log should not run out, since DB2 will reuse the older logs in a circular fashion.
In fact, unless you use infinite logging (which is risky unless very carefully monitored) then you have the same limits with archive logging.
Obviously with circular logging you sacrifice point-in-time recovery, that's the trade off.
Regards, Jeremy