Yes! you should apply for membership at the earliest... whether u apply for cop or not...
you can hold part time COP only after permission from Institute and you have to submit the details of Job to institute ... name of co. appintment letter...Holding part time cop will also give good fruits in future in applying for Fellow membership after 5 years
and if you are in job please preseve all the 1. offer letter 2. acceptance letter 3. copy of accepted resignation 4. Experience certificate 5. releaving letter (as these may be required later on becoz you are giving details of joining to institute, and you may require these documents after leaving of job.)
it is good that if you apply for part time cop with Membersip