Is a digital image of a check e-mailed to someone a negotiable instrument?

That's a huge "maybe".

Banks in the US reserve the right to reject physical checks without magnetic numbers. And they'd quite reasonably hesitate to accept anything as easily counterfeited ad a check from a computer printer.

On the other hand, some banks now have a "deposit by cell phone or scanner" service, which might be able to sneak such a check through.

On the other other hand, those banks reserve the right to demand the original check for months after the deposit; if they do so and all you can show them is a photocopy/printout they may retroactively refuse it and take whatever action the deem necessary, up to and including legal.

Basically: It probably isn't worth trying.

I haven't found definitive proof, but I have found evidence that (at least in the U.S.) it's perfectly ok to send an image of a check if both parties are aware that the check will be treated as if it were scanned and submitted electronically.

Scanning a check and submitting it for electronic payment is allowed as long as the payee is notified.

In the OP's case, the sender of the check is the one scanning the check instead of the recipient, that's the only difference from the "normal" practice for electronic checks. Once the check clears (I've seen 10-14 days as a recommended holding period) it's ok to destroy the original.

Me, I'd have no issue scanning a check and sending someone the scan for them to deposit via mobile phone, etc. Although it's a lot easier these days to simply pay by email (a lot of U.S. banks support P2P payments via email with no fees.)

Is it legal? Yes. Will it work? Probably not.

A check is an order by an account holder to their bank instructing the bank to pay a specified amount to a specified person (or to bearer). Features such as routing number, account number, or check number are conveniences that banks use to make negotiating the checks easier, but they are not legal requirements of the check. I can handwrite an order to pay John Smith one hundred dollars drawn from ABC Bank on a piece of blank paper and there is nothing illegal about it.

Just because it's legal does not mean the bank will accept it. They can refuse any check they deem questionable or possibly counterfeit. The bank will likely require a "normal" check with standard security features, such as magnetic ink and uniform size. My hand-scribbled note will likely not pass muster.

Likewise, your emailed-then-printed copy will also likely face heightened scrutiny. It is entirely within the discretion of the bank to accept it or not.

You might also want to read up on the Check Clearing for the 21st Century Act (Check 21) It was signed into law on October 28, 2003, and basically opened the door for electronically transmitting checks without requiring the transmission of the original paper version.

Check 21 is designed to foster innovation in the payments system and to enhance its efficiency by reducing some of the legal impediments to check truncation. The law facilitates check truncation by creating a new negotiable instrument called a substitute check, which permits banks to truncate original checks, to process check information electronically, and to deliver substitute checks to banks that want to continue receiving paper checks. A substitute check is the legal equivalent of the original check and includes all the information contained on the original check. The law does not require banks to accept checks in electronic form nor does it require banks to use the new authority granted by the Act to create substitute checks.

A lot of large retailers are already doing essentially the equivalent of what you asked. Be aware that there are requirements for substitute checks that you need to meet to do this. and the bank isn't required to accept it.

I recently had a friend who was sending me a cashier’s check send me photos of both sides before he mailed it. I used my bank’s mobile deposit app on my phone to take a picture of the front side photo from my iPad after covering the flash to eliminate glare. The backside was more challenging, as I endorsed the check by wrapping the iPad in saran wrap and writing over the endorsement space with a fine point permanent marker. My bank cleared the check the same day. My daughter pointed out that I could’ve simply marked it up with a signature. I did this afterwards as well, as an experiment, and would recommend taking a screenshot of the check image with an iPad, because it allows you to zoom in closer during markup and avoid a fat finger signature.