Yes, it will just take the initial 512 word pieces. Everything after that is ignored.
It depends on your specific task if this is a problem. Often, you can judge from the first 512 word pieces if a text is relevant for the query or not.
When you split it up into multiple paragraphs, you usually don’t keep the context. Often, keeping the context is not really needed as you can judge quite good from the paragraph if it is relevant to the query or not.
If you have a title (e.g. like you have it for wikipedia), it can make sense to encode it with title [SEP] paragraph. This keeps some of the context.