Does this affect spells drawn by things like Morgana le Fay and the Omphaloi?
Yes. Though those cards end up in another zone, they count as being drawn by the player, and will count against the one spell that can be drawn per turn. For example, if a player draws a site at the start of their turn and then plays Morgana le Fay, Morgana will only draw 1 spell into her hand, resulting in a total of only 1 spell drawn by that player that turn. See the Only It Can Cast entry for more information.
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