Can Tyvec be used in lieu of building paper? Can both be used for extra protection?
It depends where it is used.
Look up the difference of Air barrier, moisture barrier and vapor barrier.
Back to building science my friend. Do you want the house to let out moisture or trap it?
Both for wire lath stucco…two layers.
Yes to the first question. Felt paper is the minimum but code allows other products. The only time I would see two layers would be two layers of Grade D paper due to it’s less durable or under stucco to create a drainage plane.
Depending on the type of siding and sheathing could influence the type of WRB. The plastic products tend to be larger which have less gaps and also come in various perm ratings. If your putting it over a solid sheathing like plywood or OSB they have such a low perm rating that the paper has little effect.
Tyvek’s main purpose is to make a spec house look pretty during construction to increase the odds of it being pre-purchased. 
I use it on every project.
I do like the rubber products for around windows and doors though.
For an exterior wall membrane, yes. It’s often not applied according to the manufacturer’s recommendations, but still better (more stable over the long term) than felt paper, which loses volatile oils over time and degrades as a result, shrinking and becoming more porous to through-wall airflow.
Excellent answer and true 
Once Tyvec is applied to the substrate the manufacturer recommends applying the veneer ASAP.
It degrades with UV rays.
It use to be within 6 months.
If not, the manufacture voids its product warranty.
I do not know if this still exists today.
I was using Tyvec in the early 1980’s when I returned from Alberta and started to building homes as an rough carpenter.
All overlapping joints need to be taped and also penetrations and protrusions sealed as well.