Hi Hiranya,

I think the effect should be indirect. I mean thr exogenous goandotropin like GnRH and hCG improve the reproductive efficiency of the treated cow (namely, ovulation, luteal function, and conception rate). Improving reproductive efficency would directly  improve the productivity efficiency of the treated cows (short days open, ......).

It would depend on the gonadotropin that is given to the cow. For example, if FSH or eCG were given and estrus occurred after treatment, milk production is likely to decrease transiently in association with estrous behavior. This is less likely with GnRH or hCG, because these tend to cause follicles to decrease output of estrogen and ovulate within a predicable span.

I attached a paper that might be useful for you.