...more on the arithmetic, but...
my own response to my posted question is: (answer) Probably not...but you never know for sure!...If pro astronomers weren't looking for something or expecting something over the past 1.5 centuries of pro-astronomy, then it may have ended up being overlooked by pro-astronomers.

How many years, during the past 150,
have pro-astronomers looked for nearby stars with galactic escape velocities?...

You would think that astronomers would realize that 230km/sec[galactic orbital-velocity in our cosmic neighbourhood] plus 121.17km/sec equals 351.17km/sec.

The galactic escape-velocity in "our- neck-of-the-woods" is:
(230km/sec) x (square-root of two) = 325.27 km/sec.

Obviously 351.17km/sec would only be
a galactic escape-velocity...IF...the angle/direction/vector of "apparent motion" for Arcturus is less than 30degrees from the orbital-vector of our own Solar-System around the center of our own galaxy.
That's where finding out the direction Arcturus is heading, relative
to the celestial-equator would be helpful.

cheers.

Jacob