Not if they all embark from a parking orbit at the same time
Arranging for intercepts is essentially not possible.
The whole idea behind a laser sail is that it's a very small force applied for a very long time to achieve a very high velocity along a very specific vector. None of that lines up with what you'd need to achieve an intercept, which would be large forces along a different vector in short times, so that you can change your orbit to match your targets.
That would need to be achieved via conventional thrusters, which means that if you launch at dissimilar times, you're stuck carrying a TON of fuel, because in order to catch up you'd need to go MUCH faster then the very fast thing, and then slow down a LOT.
However, if they are launched in formation, they should have very similar relative speeds. This is identical to 'floating' next to eachother in similar orbit. The energy and fuel necessary to bring the pieces of the craft together after the desired orbit has been achieved should be fairly minimal, because their orbits will all be extremely similar.
This answers the logistical orbital questions, but it completely elides some, serious, larger concerns about this plan:
- You are accelerating via laser sail, which means you will be accelerating for a very, very long time
- You are bringing humans along
- A laser sail cannot be reversed
So, you have at least one manned ship in this fleet that needs to carry supplies and living quarters for the crew, and those supplies must last for at minimum, the entire duration of the acceleration, which is likely measured in years.
You're traveling at .1C relative to where you left, which is almost certainly a relative speed to the destination body that is a significant fraction of C. This also means that any mass that you pass along the way probably also has an enormous relative speed, which means gravitational capture or reverse slingshot is essentially off the table - You're going too fast for that to work.
You could use a laser sail to slow down, and launch a really powerful laser ahead of your crew - But you don't have one large enough for the new giant craft you just built.
Assuming you manage to engineer a solution to the issue of supplies, you still have a crew that is basically riding a space bullet with no brakes. You need an alternate system of propulsion capable of supplying the same order of magnitude of delta V that your construction fleet received from your space laser array - Which brings to mind the question of why you didn't just embark with one of those instead.