No. OTW memberships and AO3 accounts are not linked in any way. To get an AO3 account, please join the invitation queue. Donations to the OTW help us keep the Archive running, so we welcome your support, but we are committed to offering AO3 as a free service for everyone. There is no connection between individual donations and accounts on the Archive.
If you have questions about AO3 invitations, please contact AO3 Support.