If company already subscribed to MailChimp do they need also Mandril to send transactional emails such as app welcome, invites to join or befriend, password recovery etc.
Can one send password recovery or welcome email as one person campaign programmatically using MailChimp alone? Or is it too expensive or too cumbersome?
I've been using Mailchimp for a while and what you are seeking can be partially managed with a featured called automation within Mailchimp. It allows you to:
For password changes notifications, email verifications and such transactional emails you could use Mandrill, but as an add-on within Mailchimp which has a separate pricing, where you can start free for the first 2000 emails.
I believe the automation on Mailchimp + a good use of their API to make changes on the list, could easily be put to good use to your advantage (haven't tried this combination yet but will do in the future, let me know if you find out something).
To answer more directly your question, yes, you can achieve a certain degree of automation with the automation part of Mailchimp (which is relatively new), but for a more granular control you definitely could use Mandrill as an add-on within Mailchimp.