Yes, you can file Form 8379 electronically with your tax return, even with a Form 1040-X (see the Instructions for Form 1040-X for more details).

Generally:

• If you file Form 8379 with a joint return electronically, the time needed to process it is about 11 weeks.
• If you file Form 8379 with Form 1040-X, the time needed to process it could be up to 20 weeks.