A monopole antenna is half a dipole, with the ground plane acting as the other half. If you miss off the ground plane then the effectiveness (and the efficiency) of the antenna will be very poor. It may therefore be too insensitive and mismatched to be of any use. By all means try it and see how bad it is, then report back.
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The x's represent the solid etch pattern on a single sided board (two solid patches, a ground patch and a radiating patch). The input is connected between the bottom central x (center conductor) and the large ground patch. The triangle should be about 1/4 wavelength across the top and about 35° apex angle. The ground patch should be about 1 wavelength or more.
This is simple to evaluate. Just connect a coaxial connector betweeen the center conductor and the ground patch. For a 1/2" triangle, an SMA connector will work fine. It should operate well from about 4 to 8 gHz. To improve Return Losss (VSWR) change the apex angle.
Another approach is a printed circuit balun terminated in quarter wave elements.
