Load Balancing in general would be useful if you need high-availability, though whether or not they'd be an ideal fit for what you're doing depends on what you actually need.
If you're planning on working with hundreds of Droplets, or potentially hundreds++, the only real way to go about this would be working with the API as configuring all of that by hand through the CP will be very time-consuming.
About Load Balancers
DigitalOcean's Load Balancers accept incoming traffic and route it to the first server configured and responding to a health check on port 80, though you do have the option of using another port or if that's not applicable, you can use TCP health checks and define the port you wish.
The order that you define/add servers is the order they will be used. So if you have 100 Droplets set to work behind a load balancer, the LB will send traffic to the first server that responds (that'd be the default Round Robin option). You also have the option to use "Least Connections" which means that the server that has the least amount of traffic will be the one to receive the next request and so forth and so on.
Will They Work For You?
They can, but again, it really depends on how you need requests to be processed.
Load Balancers can handle traffic distribution, though how you'd set things up for what you're wanting to do really depends on how the processing is being handled.
Knowing a little more about how your wanting things to work, or how they are working would be very helpful in determining whether or not using a Load Balancer would be ideal, or if there's a better way to manage.