As far as I can tell, yes. If cookies (or other means of storing data on the users computer) are strictly technically necessary, and no data collection takes place as a legitimate interest, and you do not process data requiring consent, neither the ePrivacy directive nor the GDPR requires you to create a cookie banner. Needless to say, I'm not a lawyer and this is not legal advice.
On a technical level this would likely mean turning off access logs and other tracking mechanisms. (IP addresses are considered personal data last I checked.)