Are HAIFA-construction based hash functions (e.g. Argon2) resistant to length-extension attacks? Would a HAIFA-construction based hash function like Argon2 resistant to length-extension attacks?

I say that Argon2 is HAIFA-based because BLAKE is, and Argon2 is based on BLAKE.
Yes. 

The HAIFA construct as introduced in A Framework for Iterative Hash Functions - HAIFA by Eli Biham and Orr Dunkelman is proposed with the explicit goal of eliminating various pitfalls of the classic Merkle-Damgaard construct.