No. The coupling constant will not change. It is the same as the chemical shift; the constant of proportionality introduced by your external magnetic field simply cancels out.
A proper mathematical justification may be more complicated though. I assume you want this, but unfortunately I cannot provide serious derivations over the Internet. The books I recommend are OCP 32, "Nuclear Magnetic Resonance" by PJ Hore, and OCP 92, "NMR: The Toolkit" also by PJ Hore, in that order.