It makes no difference whether the scion comes from the tip of a leader or a branch; you can graft either to a branch or to make a leader. Grafting a dormant scion to a tree that has broken dormancy is the standard procedure for grafting to established trees. Bench grafting is usually done with both rootstock and scion still dormant. Grafting a scion which has broken dormancy usually fails because the awakened scion needs a supply of water/nutrients from the rootstock and does not have time to callous in and establish the necessary connections. Swollen buds means the wood is breaking dormancy, but during the earliest phases, grafting may still work. The time it takes to show growth if the graft takes varies depending on the species and can vary between grafts of the same species. Generally two to three weeks for peach scions to start pushing leaves. You did not pick the easiest species to try your first grafting experience on. Peaches are more finicky than many others. If they fail, don't be discouraged, next time try pears or apples and cut your teeth on these. Beginners have the best success with them.

Thanks Dave for precisely answering my questions.