He did that in the old testament and to an extent he is currently doing that until the times of the gentiles are fulfilled. The hiding himself could be in regards to less direct intervention and natural protection you would have; With his face being in your presence.
I don't know about that, but I know man cannot hide himself from God (Psa. 139:7-10) under the old or new covenant. Man cannot go anywhere from the presence of God. We as believers have been bought with a price (1Cor.6:20), and He said He will never leave us nor forsake us (Heb. 13:5).
God hid His face from Israel because of their sins (Isa. 59:2); but He lives inside of us, "only," because we have "no sin" (Col. 2:11) and we have His Spirit living inside our hearts (Eze. 39:29). It's interesting because out of the heart proceeds unfruitful works, but God said, He will never leave us, neither will He leave our hearts (Mat. 15:18, 19).