Excellent question - short answer: hypothetically yes, but we would know it is cancelled out depending on its distance/environment/companions.
 
First, we need to divide space into two stages - low redshift and high redshift which can be interpreted as: present time(13.8 by old universe), young universe. 

present time = redshift from the expanding of the universe is z=0, as we go back in time redshift grows. 

Now, in the local Universe, we can observe stars and all variety of stuff out there while in the high redshift we are bound to galaxies and all sorts of raging formations. The farthest single star that was detected (in 2018) is on redshift z =1.5 (9 billion light-years away.)

Also - another thing that needs to be mentioned - things in space tends to cluster. and here are two images for that
Actual Survey of galaxies  (observable universe - obviously) 
<img src="http://www.2dfgrs.net/Public/Pics/2dFzcone_big.gif">

3D simulation of the cosmic web structure 
<img src="https://www.universetoday.com/wp-content/uploads/2010/12/cosmic_web_3smaller.jpg"> 
we can see that galaxies(every light dot) tend to group up together into nodes and filaments - but there is also the dark patches - called voids.

Why am I talking about this  - Simply because it is very rare that we have wanderer stars and systems. It's all somehow grouped and organized - when it is organized (for example star clusters) all the stars inside tend to have relatively the same properties, and they are on the same distance(cosmological redshift) - if there is a star inside that is going nuts (blueshift) we would see it as bluer than all other ones (unless we do the cosmological redshift reduction - then there would be some in blue some in red).
To conclude we expect blueshift in our local universe, where we can observe motion of stars/planets. 
For example if we look in the andromeda - all the stars in there have blueshift (even tho 50%(random number) of stars have different true and radial velocities).  It is the same with cosmological redshift - it dominates, but we can subtract it - and get their velocities.

I hope any of this makes sense - but here is an awesome video you have probably already checked upon :)

https://www.youtube.com/watch?v=rENyyRwxpHo