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You can setup "UsefulFunction[a, b]" to use custom infix notation "a [LeftRightArrow] b" as follows:

Needs["Notation`"];
AddInputAlias["4" -> ParsedBoxWrapper["\[LeftRightArrow]"]];
InfixNotation[ParsedBoxWrapper["\[LeftRightArrow]"], FlatJoin];

But using a unicode character that does not have a mathematica definition (e.g. "\[name]") such as ":27d7" gives you an error:

Now the syntax highlighting is broken, and that is really my question: how can you tell mathematica to correctly syntax highlight new unicode infix operators?

(Note: the messages can by avoided by adding internal information on the character as follows:

Notation`Private`internalCharacterInformation["⋗"] = {"0x2295", "Infix", "450", "None", "3", "3", "MyOp"}; InfixNotation[ParsedBoxWrapper["⋗"], FlatJoin]

Edit:

I'm now pretty sure that the answer will involve editing /Applications/Mathematica.app/SystemFiles/FrontEnd/TextResources/UnicodeCharacters.tr

and adding something like

0x22D7      \[FlatJoin]     ($fj$   $&FlatJoin;$   $\oplus$)        Infix       320     None        4       4

and then using the Notations package...

You can setup "UsefulFunction[a, b]" to use custom infix notation "a ↔ b" as follows:

Needs["Notation`"];
AddInputAlias["4" -> ParsedBoxWrapper["↔"]];
InfixNotation[ParsedBoxWrapper["↔"], FlatJoin];

But using a unicode character that does not have a mathematica definition (e.g. "\[name]") such as ":27d7" gives you an error:

Now the syntax highlighting is broken, and that is really my question: how can you tell mathematica to correctly syntax highlight new unicode infix operators?

(Note: the messages can by avoided by adding internal information on the character as follows:

Notation`Private`internalCharacterInformation["⋗"] = {"0x2295", "Infix", "450", "None", "3", "3", "MyOp"}; InfixNotation[ParsedBoxWrapper["⋗"], FlatJoin]

Edit:

I'm now pretty sure that the answer will involve editing /Applications/Mathematica.app/SystemFiles/FrontEnd/TextResources/UnicodeCharacters.tr

and adding something like

0x22D7      \[FlatJoin]     ($fj$   $&FlatJoin;$   $\oplus$)        Infix       320     None        4       4

and then using the Notations package...