StoreFront is a domain-joined Windows Server and NetScaler on the other hand is a non-domain joined (FreeBSD with a twist) appliance.
I think there is or was an option to store ones credentials for GW auth, but that's more or less the same as storing your credentials in web browser.
If you want 1:1 experience I would expose the SF VIP and allow clients to authenticate with it and use Optimal HDX routing in StoreFront to pipe the HDX traffic via Gateway. This ofc is just for internal network.
If you need a more modern SSO experience with (or without) GW, I would urge you to look in to federated authentication (SAML/OIC).
Are the users accessing the environment from an internal network or from the internet? If internal network, what is the reason not to expose the SF VIP?