Would a time-trial a week have the same effect?
C
A time-trial is a race against the clock and definitely should be an intense, sustained effort, but you have to pace it and not work flat out from the start (unless it's a very short tt). The problem is, unless you judge your effort properly, you'll either burn out early or finish with some gas left in the tank. Also the tt is an extended effort and not the best way of training, because you'll not be lifting your overall top speed.
You will improve your times in the tt over a period if you keep doing them along with a reasonable mileage in other runs. However, a session of hard intervals, done regularly with proper recovery between sessions, will improve your basic speed more quickly. The session doesn't have to be too formal - use a series of lampposts, favourite stretches of road, or go hard on all the hills on one of your routes - whatever suits you and where you are riding. Along with the hard work, possibly the harder thing to do is to ride relatively slowly on recovery rides after a hard session or a tt - because that's when the hard work is consolidated.