Short answer: no, that will not solve your problem even if you could fully calibrate the display to Adobe RGB (1998). Again, non color managed applications have no idea what Adobe RGB (1998) is. It's like you asking me "How far do you live from my home" and I reply "1000". Is that 1000 feet? 1000 miles? 1000 kilometers? Without color management, RGB numbers have no defined scale and the display conditions are not known. So not, that's not a fix. The fix is always viewing image data in color managed applications, using data with a defined scale (embedded profiles) and using a calibrated and profiled display.
You cannot control what your clients see unless they have the same kind of reference display system you have, calibrate and profile identically AND use color management to view the image data. That's why such high end reference display systems from compaines like NEC (SpectraView) and Eizo exist.
Lastly, having a wide gamut display who's color gamut is Adobe RGB (1998) doesn't mean it's producing Adobe RGB (1998)! There is far more to any such color space than just it's color gamut. Alter the white point, it's not Adobe RGB (1998). Alter then cd/m^2 and it's not Adobe RGB (1998) or sRGB.