Not when you have multiple citizenships.
When that's the case, in order to represent a country in IIHF competition a player must satisfy the following:
- Participated in competitions on a consistent basis in said country over 16 months (480 days). That 16 month period must occur over 2 seasons after the player's 10th birthday.
- Resided in said country for that 16 month period.
- Didn't transfer to another country or play for a team registered in another country during that 16 month period.
Knies doesn't meet any of those conditions for Slovakia so he cannot represent them unless he moves to Slovakia to meet those conditions or applies for and receives an exemption from the IIHF.
Those same conditions apply even if he were to say renounce his American citizenship too.
The most notorious example of a player getting an exemption is William Nylander. He was born in Canada, raised in the US, and a dual citizen of Canada and Sweden. He could only meet the aforementioned conditions for the US (non-citizen). He wanted to represent Sweden but since he didn't meet the conditions, he applied for and received an exemption since he couldn't meet the conditions for either of the countries where he had citizenship.
The Knies case is pretty straightforward so while he could apply for an exemption, I doubt the IIHF would consider it, especially as Knies has always represented and tried to represent Team USA.