Buds are never really inactive, unless you're grafting over the winter. If you mean that they aren't actively pushing, that is not a problem as long as the budwood and its foliage have hardened.
When you graft mango budwood, the scion first needs to establish cambium bonding, which starts to take place within the first couple of weeks. Once the cambium of the scion has fully bonded to the rootstock, the scion will stay alive nearly indefinitely. Assuming the rootstock has leaves or is thick enough to have built up energy reserves (or is newly emerged from a seed, which has enough energy for about 2 flushes), the scion's buds will eventually swell and flush.