No, there isn't any block feature on the main site, only in chat.
If a particular user is pinging you excessively, just ask them to stop. If they don't stop after being asked to, flag for moderator attention and explain the situation.
To some extent the absence of such a feature is intentional. Ignoring users that misbehave doesn't actually solve the problem, those users can continue to misbehave towards other users that don't have them blocked yet. If a user doesn't stop problematic behaviour after it was pointed out to them, a suspension might be necessary. So the mechanism to deal with such users are the moderators that handle exceptional situations, which makes a blocking feature for this use case superfluous.