I assume you mean the Virtual Console, as the eShop is just the name of Nintendo's digital store. Nintendo has said the Virtual Console banner won't be coming to Switch, but there was no confirmation that old games would never be re-released in some form or fashion on the system. The most prominent online leakers, who had divulged more or less all the technical details about the Switch months before it launched, claimed that a few Gamecube games were known to be compatible, with the expectation that this functionality would be available at some stage.
What surprises me more is that video services like Netflix and Youtube aren't available. You can use them on 3DS, Wii and Wii U, yet the newest device doesn't support them yet. Another strange thing is that the Switch has a web browser that's only accessible by exploiting a workaround. For some reason, though, the console officially doesn't support web browsing.