In some instances, your wholesale price will be affected by putting the item on sale through Shopify. In other instances, it will not.
If you are using a Percent Off discount for the wholesale price, then the answer is yes! If you change the price of your item by adjusting it's listing price directly via the listing settings, any discount rules on this item will now apply to that new, lower sale price. So if you have an item that is normally priced for retail at $10.00 and apply a wholesale discount rule to it for 10% off, your product’s wholesale price would normally come out to $9.00 (since 10% of $10.00 is $1.00). If you put said item on sale through Shopify’s listing price editing feature to bring the retail cost out to $8.00, your wholesale price will now be $7.20 (since 10% of $8.00 is $0.80).
Set Price discounts will not be affected by changes to the retail price of the product (unless the retail price is already lower than the discount you're setting, at which point that lower retail price will be applied). Your wholesale customers will be unaffected by most retail discounts, such as discount code style sales, so you are welcome to use those as often as you'd like without worry that wholesale customers will receive further discounts.
That being said, BOGO discounts are the one exception to this rule; these will affect wholesale customer's carts, duplicating the items within. If you wish to use BOGO discounts for retail sales, you will need to create a customer segment that *excludes* wholesale customers, which you then apply to said BOGO discounts. This will effectively prevent this bug from affecting wholesale carts and customers.
If you do notice other discounts applying, feel free to email us at firstname.lastname@example.org and we can take a closer look to help figure out what's happening.