Of course they can, just like fiats co-exist now.
https://bitcointalksearch.org/topic/m.1998973
Topic: Can Bitcoins and Litecoins (or other alt currencies) co-exist? - page 2. (Read 2834 times)
It would be safe to say that they can indeed coexist. In fact, it may prove to be the ideal situation. At the moment, BTC dominates in value and size of user base, but that could just be the "first to arrive" advantage.
Can dollars, Euros and Yen coexist?
At the moment I think we could say that Bitcoin is to Litecoin what Gold is to Silver. Is it safe to assume they can co-exist? If not, why?
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