HaProxy will redirect client connections to one of the backend nodes, depending on configuration. If all nodes are configured equally (round robin), yes, the cluster may accept total around 3 x max_connections. But I’d expect at least some uneven traffic distribution and effectively it may be bit less.
Remember that proxy node may need some TCP stack tuning when dealing with large number of total connections.
Btw, completely different situation is with ProxySQL, which is more then just regular proxy, and has it’s own connection pool. Thanks to multiplexing, it can actually accept many times more connections then total max_connection all backends offer.