Moz's spam score will not directly affect your Google ranking, no.
Moz's spam score is their inhouse metric designed to measure how spammy they deem a domain to be. It is formulated by measuring 27 common factors.
The main metric being similarities between other websites which have been penalized by Google. The 27 common factors include (according to Moz)
1. Low number of pages found
2. TLD correlated with spam domains
3. Domain name length
4. Domain name contains numerals
5. Google Font API Present
6. Google Tag Manager
7. Doubleclick Present
8. Phone Number Present
9. Links to LinkedIn
10. Email Address Present
11. Defaults to HTTPS
12. Use of Meta Keywords
13. Jumpshot Visit Rank
14. Rel Canonical
15. Length of Title Element
16. Length of Meta Description
17. Length of Meta Keywords
18. Browser Icon
19. Facebook Pixel
20. Number of External Outlinks
21. Number of Domains Linked-To
22. Ratio of External Links to Content
23. Vowels/Consonants in Domain Name
24. Hyphens in Domain Name
25. URL Length
26. Presence of Poison Words
27. Uses High CPC Anchor Text
(info provided by Moz: https://moz.com/help/link-explorer/link-building/spam-score)
A high spam score doesn't instantly mean this website is trash. It means this website has similarities with websites that are indeed trash, and have been deindexed and/or penalized by Google.
So, although Moz's spam score isn't airtight, it's a good indicator that you should look at your website from a quality perspective and try to improve it.
It should be noted that all metrics should only be used as a guide - they are not set in stone!