Can Forms 2848 and 8821 be e-signed?

Short answer: yes, but only when you submit them through the IRS online tool; mailed or faxed forms need handwritten signatures.

E-signed 2848s and 8821s go through "Submit Forms 2848 and 8821 Online".
Form 2848 needs the taxpayer and the representative; 8821 needs only the taxpayer.
If you have no prior relationship with the client and they sign remotely, verify their identity first; for clients you don't know who sign in person, verifying is recommended.
Check the IRS page "Submit Forms 2848 and 8821 online" for current rules.