No, to do the infamous "walk away" split, you must have <3 day old larvae in the queenless portion. The brood oval must be split to provide a reasonable assurance of young cells.
If your upper box and lower box both have a portion of the brood oval and that portion is actively being laid into, then yes, just splitting the hive will work. However, by June many hives are entering the backfill period, and the upper box will be free of young larvae. In that case, the upper half will be unable to raise a queen, and the bees that are carried over in the box will be foragers and not nurse bees.
Inspect the frames and assure yourself you have just laid eggs or recently hatched larvae in both portions (or move frames to create this condition).
Be aware that a walk-away require 16 days to hatch a queen, about 7 days to mate and begin laying, and 20 days to the very first cohort of new brood. In the inter-regnum the hive will dwindle. What will your flow be like in 45 days? Will you be in a July dearth? There is also a 25-30% chance that the virgin queen won't take, and the hive will extinguish. If you have 40 hives, the casualty rate is immaterial, if you have one, it represents a big potential loss.
The internet guru that has popularized walk-away splits uses narrow hives and short boxes and top entrances, this generates a "chimney" brood pattern. The chimney increases the likelihood that a blind shuffle split by box will have appropriate young larvae. The downside of the particular box-frame-entrance prescription is that it makes other management more difficult.
Buying a queen, though not free, results in a nearly uninterrupted transition through June. June should be the peak of your honey production, so the $20 queen will be more than paid back by production. You lose money in the walk-away.
So-called "Russians", several generations away from the pure inbred Vladivostok lineage, are going to be American mutts. The Vladivostok bees can trace lineage back to Ukrainian steppe bees that had a lot of "Italian" genes in them anyway. "Russians" are more a marketing term than a genetic descriptor for bees that are not created from known crosses.