An older variant for some long i, yes. Classical Lat. <ī> is thought to root from PIE <*ei>, in cases where it renders also <ει> in Greek.
But classical Latin <ī> also roots from PIE <*iH> (i immediately followed by any of the so-called laryngeals)... In such case, you'll not find -I presume- <ei> as a variant in ancient Latin or in proto-Italic inscriptions.
I would say that <ei> becoming <ī> isn't that much different than <ai> and <oi> ending as <e> in inscriptions (through <ae> > <æ> and <oe> > <œ>, respectively).
To spell it <ei> in a 1580's Bible might perhaps be a way to indicate the pronunciation without marking diacritics such as <î> or <ī>, couldn't?