The general thought is, if you're comfortable asking an INFJ how he/she is doing, go for it. I think INFJ's like interaction. But if they don't trust you or don't feel compatible with you, they're only going to be open with you up to a point. And if you push for deeper interaction, they'll withdraw from you - at least, this is my style of drawing boundaries. (If necessary, I would withdraw indefinitely.) In general, I think INFJ's dislike any level of judgmentalism, incompatibility, or disapproval. They may humor you to the extent that they want interaction, but they will keep their distance until they deem otherwise. Tolerate an INFJ's need for privacy and compatible friendships. Don't force your care on someone, but by all means, if you care, then I see no reason to go ahead, but don't expect them to want your level of care.
If your agenda is to "prod" them to get help, you're really doing more psychological harm than good.
From my experience, INFJ's will seek help from the people they trust, even if they need help and haven't found the support they need. They like non-intrusive, friendly, consistent interaction. Don't try very hard to ask them about personal questions, because they will share when they are ready to share. Period.