Short answer: No.
Essay form: ArcSDE isn't a database, it's an interface to databases. The only
way to change table column order with the ArcSDE API is to export in the desired
order and create a new table with the result. If, as in your example, you can
coax the database to reorder the columns, then ArcSDE will present them in that
order, but a brief web search indicates that SQL-Server, PostgreSQL and Oracle
do not permit this as a trivial operation. Many of the referenced links recommend
using a view, which will work, but ArcGIS puts limits on geodatabase participation
by views. If you're going to have to reload the table anyway, consider doing some
row-order optimization as well, by exporting in spatial index order.