My goal is to figure out if i'm better off with one strong server, or multiple weaker servers with a load balancer. Does the fact of splitting the load between servers have an effect on the total load my website could take?

It's hard to single that out, because there are of course a lot of parameters that affect the results, so some assumptions:

• Putting failover considerations aside - I know it matters, but for the sake of the question's simplicity, lets assume nothing fails.
• The servers in the multiple servers option have an accumulated "power" equivalent to the one server option (about the same amount of cores and RAM space).

If that is too theoretical, here is a concrete question that could help:
Suppose I have several instances of exactly the same server - lets call it S.
Suppose that server S can serve a load of up to X calls per time unit.
Will two S servers with a load balancer serve 2X calls per time unit? significantly more? significantly less?