If we agree to research D:AP with the spartans, then our research would be tied to that. We'd both need to research the same tech for leap frogging to work.
The basic idea is that faction A researches tech 1, while faction B starts on the same tech. Faction A finishes that research, starts on tech 2. A sends B tech 1, and B starts on tech 2, with no penalty for switching etc. B gets 2, sends it to A, starts on 3. A also starts on 3, gets it, sends it to B etc. etc.
It doesn't necessarily work with factions with massivly uneven tech rates, since in that case it's possible that A could research techs 1 and 2 before B could. If that were the case, then we'd be foolish to enter into that sort of leapfrogging, since we'd get little gain, and we'd be better researching the end goal solo.
However, I think that we should try for closer relations with the Spartans. Going for a joint tech project like this one takes a lot of trust, and I think we should suggest a pact. This would be great for our research, income etc, give us lots of info on the spartans (And them on us, but that can't be helped.) and give us an ally against the almost inevitable push by the other factions.
Without the pact, I think we should go solo on D:AP (we need 3 techs I think, so we could reasonably assume something in the order of 15 years, 2165 wouldn't seem too unreasonable) with Bioengineering as our goal immediatly afterwards. Get as many probes in the water as we can, and probe rape the spartans for every tech they have, infiltration data etc. No pact = no friend.
Edit: Haven't voted btw yet