Can I e-file after mailing my return?

I recently mailed my return (for a prior year) and then realized I made a huge mistake (accidentally claimed depreciation on an asset that I wrote off fully a few years prior)

Do you think it's a good idea to efile an updated return right away? My reasoning is that the efile will get there sooner than the mail and they'll start to process the efile first, and then when they finally get the mailed return they'd just treat it as a duplicate and toss it or something?  (or would that backfire on me and create a red flag of some sort?)

If not that, then should I file an amendment right away or do I have to wait until the mailed return has been assessed and then amend it?