Short answer
In total, yes, and almost in proportion. In 856,699 posts from 112 party pages and 74 leaders' pages in 20 European countries, a month with twice as many posts brought roughly 1.9 to 2 times the interactions.
What the evidence shows
- Engagement per post did not fall in the basic comparison, and fell by about 5% for each doubling once each page's long-run trend is allowed for.
- On days when a page posted more than it usually did that month, each post drew about 13% less for each doubling.
- Posts made within an hour of the page's previous post drew about 12% less.
- The monthly pattern held across the decade, for large and small pages, campaign and other months, and populist and other parties, and was stronger for leaders' pages.
Caveats
Pages may post more when they expect more interest, so these estimates describe how engagement moves with volume, not the effect of deciding to post more.