Would sidechains help Bitcoin scale? Are sidechains intended to help Bitcoin scale? Do they reduce load on Bitcoin's main chain?

If not, why not?
No. They can increase scale, but that is not what they are good at or intended for.

Before giving a longer answer, let me first talk briefly about the difference between scale and scalability.

Increasing scale means increasing the throughput or number of participants to the system. It's very easy to achieve (decreasing the time between blocks, or increasing the size of blocks), but it would come at a cost of higher centralization pressure for mining and increased validation cost to the system. Whether these increased costs are acceptable is controversial, but there are certainly costs involved.

Increasing scalability means changing the system in a way such that increased scale comes with less increased costs. Known mechanisms for better scalability include better peer to peer relay protocols, faster digital signature systems, software improvements, technology on top such as payment channels or lightning to reduce on-chain transaction need, ...

Sidechains don't improve scalability. If we want the same security level with sidechains, the same amount of people and miners need to be validating them. That is at least as costly as just increasing the block size of Bitcoin itself, and sidechains come with extra compromises on top of that.

So, sidechains may increase scale, but are not better at it than larger blocks would be.

What sidechains do bring is the ability to experiment. To be able to build networks that run on different - and possibly better-scaling - technology, but without needing to first beat bitcoin's (the currency's) network effect.

Sidechains are intended to improve scalability, but only indirectly: by enabling innovation. Not because they can just offload things from Bitcoin.