Can one size chart cover several categories, like T-shirts and Polos?

Yes. Open Plugins → Size Charts, click Edit on the chart and type all the category IDs into Assign to category IDs, separated by commas (for example 5, 9). Click Save.

Every product in any of those categories then shows the same chart. You can combine this with Assign to product IDs for single products elsewhere in your catalog. The Assigned column on the list shows how many products and categories each chart covers.