Log download user rol

No, not specifically. You can adjust the access to all settings pages with relevanssi_options_capability, which includes the log page and access to the log download.

What you can do is to grant access to the settings to a lower role, but then use the relevanssi_tabs hook to remove settings tabs from users who are not allowed to see them. This way you could allow all editors to access the settings, then remove all tabs from them except the “Log” tab.