This is a purely theoretical question, because I suspect that trying to build a launch system of this sort would pose its own set of very complex problems.
That said, the Wikipedia page for the English Electric Lightning notes that while it was popular at air shows to do the "party trick" of taking off and immediately standing the plane on its tail to show off its ferocious vertical climb ability, while on active duty doing a real intercept, time to altitude could be significantly reduced by taking of, accelerating horizontally to ~430k kts IAS, and only then pulling the nose up to achieve the vertical climb.
Ignoring for a moment how we might actually achieve this goal, but could a similar launch profile help a rocket trying to reach LEO or above? Accelerate horizontally using the rocket for power on some sort of support system (such as wings) which then curves the rocket up to a vertical direction only after a decent speed has been attained.