Can WooCommerce accommodate limited period sales? For example, a January Sale, Weekend Deal.

Yes, it is possible to promote and administer all types of sales. There are lots of options and lots of different ways of achieving this. Examples include a Discount Code that can be used shop wide or applicable only to a specific category. It is also possible to manually apply a sale price to a product which will override the regular price of the product. This works well where the sale is only for a small number of products.
WooCommerce Frequently Asked Questions