Can I edit the SEO titles and descriptions of many products at once?

Yes, with Settings → SEO Settings → Bulk SEO Editor (part of the Advanced SEO plugin). It shows your products in a table with a Search title and Search description box for each:

1. Use Filter products to narrow the list (it loads up to 100 products at a time).
2. Edit the boxes you want. Changed rows are highlighted.
3. Click the Save button at the top once (it shows how many changes you have made).

A counter under each box shows the length against 60 characters for titles and 160 for descriptions, which is roughly where Google cuts them off. Going over is allowed; it just gets truncated in results. Only the title and description are saved, so nothing else on the product is touched. If any product fails to save, the message names it. Changing the filter before saving discards unsaved edits.