Does this work only for symbols or also for strings

[Kreijstal]

Does this work only for symbols or also for strings

[jkuczm]

Currently builtin TeX conversion, of boxes embedded in strings, is not modified by TeXUtilities package.
Builtin conversion works by changing string-embedded boxes to ordinary boxes, and converting those ordinary boxes.
Converter never sees expressions represented by those boxes, that's why Format definitions, which are set at "expression level", are not used.

We can modify one of definitions of relevant converting function, to force reinterpretation, of string-embedded boxes, as expressions, then convert those expressions.

Import@"https://raw.githubusercontent.com/jkuczm/MathematicaTeXUtilities/master/NoInstall.m"

System`Convert`TeXFormDump`maketex[
  str_String?System`Convert`CommonDump`EmbeddedStringWithLinearSyntaxQ
] := (
  System`Convert`CommonDump`DebugPrint@"------------------------------------";
  System`Convert`CommonDump`DebugPrint@"maketex[str_String?EmbeddedStringWithLinearSyntaxQ]";
  System`Convert`CommonDump`DebugPrint["str: ", str];
  ToExpression[
    System`Convert`CommonDump`RemoveLinearSyntax[str, Recursive -> True],
    StandardForm,
    Function[, Convert`TeX`ExpressionToTeX@Unevaluated@#, HoldAllComplete]
  ]
)

Format[OverVector[x__], TeXForm] := TeXCommand["vec", {x}]

Now both:

TeXForm[\!\(\*OverscriptBox[\(x\), \(\[RightVector]\)]\)]

and

TeXForm["\!\(\*OverscriptBox[\(x\), \(\[RightVector]\)]\)"]

should give \vec{x}.