multiple table scan performance

I've got some functionality that necessarily must scan a relatively large
table. Even worse, the total workload is actually 3 similar, but different
queries, each of which requires a table scan. They all have a resultset
that has the same structure, and all get inserted into a temp table. Is
there any performance benefit to revamping the workload such that it issues
a single:

insert into (...) select ... UNION select ... UNION select

as opposed to 3 separate "insert into () select ..." statements.

I could figure it out empirically, but the queries are really slow on my dev
laptop and I don't have access to the staging system at the moment. Also,
it requires revamping a fair bit of code, so I figured it never hurts to
ask. I don't have a sense of whether postgres is able to parallelize
multiple subqueries via a single scan