No
You cannot include GNU Affero GPL v3.0 code in a BSD 2-Clause License-licensed project and ship the result under BSD 2-Clause License. GNU Affero GPL v3.0 requires the combined work to be distributed under GNU Affero GPL v3.0 (or compatible). If your project is meant to stay BSD 2-Clause License-only, do not include GNU Affero GPL v3.0 code in it.
| License | Family | Patent grant |
|---|---|---|
| GNU Affero GPL v3.0 (AGPL-3.0) | network-copyleft | Yes |
| BSD 2-Clause License (BSD-2-Clause) | permissive | No (implicit at most) |
GNU Affero GPL v3.0: GPLv3 plus § 13: providing software over a network triggers the source-disclosure obligation.
BSD 2-Clause License: Two-clause BSD: very similar to MIT, no patent grant.
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