The second sentence of the definition Obstruction reads "An object that can be safely passed on only one side and an area so designated by the sailing instructions are also obstructions. Based on this my answer is YES, an area designated in the sailing instructions can be considered an Obstruction even though it does not qualify as an object according to the Oxford Dictionary.

Complementing the Comment by Claudio Uras, RRS19 and 20 will apply at the boundaries of an area even if they are virtual, in the sense of being defined by coordinates. We don't want boats to sail, for example, into prohibited military zones or cross borders between warring countries, even by one inch.

Agree with the two of you

In a similar vein, can you declare an area as an obstruction in the SIs that sailors must not enter even when they’re not racing. For example, an area of our lake is a nature reserve in which Sailing is not permitted. Or do the SIs only apply during racing?

No need to write it in the SIs. Local regulations should be enough.
No penalisation by juryn though.

Responding to "no need to write it:"
US Coast Guard in Seattle is requiring that Traffic Zones rules and Marine Mammal rules be included in the NOR or SI.
The harsher version, if so not included, is that each competitor sign each of the Traffic and Mamma rules!
So your best bet is to go ahead and include your marine sanctuary as an Obstruction in the SI.

Thanks - our current practice is to include all such areas as obstructions in the SIs.