Boro are in the semi-finals of the Senior Cup, with a trip to Marske United yet to be played.
The news is also a potential boost for Saturday League side Itis Itis Rovers, who are through to the Saturday Challenge Cup final, and Newlands Park, who qualified for the Sunday Challenge Cup final.
The NRCFA statement said: "Following The FA’s statement yesterday announcing the conclusion of the 2019/20 football season, the North Riding FA Board of Directors met this morning via video conference call to discuss the implications for football across the county.
"The Directors of North Riding FA agreed to support The FA’s strong and clear recommendation that leagues should consider expunging all results for the 2019/20 season in line with the National League System and Women’s Pyramid.
RETRO SPOTLIGHT: 15 nostalgic Scarborough photos from the Scarborough News sports archives
Scarborough Athletic slip to 2-0 defeat at Brackley Town in National League North opener
Ebberston battle back to sink hosts Filey in SBL Premier Division thriller
Commonwealth Games 2022: Scarborough's Chris Turnbull and Team England win bowls mixed para pairs bronze medal
Jack Carradice-Clarkson takes 6-11 as Flamborough sink Wold Newton
"Following this guidance, we believe, will allow for consistency across the grassroots game in North Riding. As a Board and staff we will endeavour to provide the utmost support to leagues over the coming weeks and months.
"It is the intention of North Riding FA to conclude the 2019/20 County Cup competitions when football resumes. This decision will be revisited on 30th April 2020 and if necessary will be continuously reviewed thereafter, in light of the current Coronavirus pandemic.
"Finally the North Riding FA Board of Directors would like to confirm that entry to our 2020/21 County Cup competitions will be free to all clubs.
"We send everyone involved in football across the county our best wishes at this challenging time and hope that you are finding ways to stay healthy in line the Government’s advice about social distancing. Please stay safe and we look forward to the resumption of football when the time arrives."