Sure, another invisible dimension sound somewhat weird, but not impossible.
Besides the Elisha example there are more hints from Scripture -
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The Transfiguration in Matt 17.
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Joh 20:19 On the evening of that day, the first day of the week, the doors being locked where the disciples were for fear of the Jews, Jesus came and stood among them and said to them, “Peace be with you.”
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1Kor 4:9 For I think that God has exhibited us apostles as last of all, like men sentenced to death, because we have become a spectacle to the world, to angels, and to men.
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1Kor 11:10 That is why a wife ought to have a symbol of authority on her head, because of the angels.
[3] and [4] are interesting, it seems that besides God angels can (are allowed to?) watch us.