No one shrimp will not hurt you bio load at all.
I kept Tiger shrimp, CRS, and cherry shrimp. I bred them too. I will say this shrimp are not easy to keep. The water has to be just right or they can have moulting issues and die. That is what I had happen. You need your water gH 3-5, kH 2, TDS 150-200. To get mine to breed I was buying RO water and adding stuff to the tank. It's a pain keeping shirmp. yes it was fun for a year but I am over shrimp.
Blue tigers are not cheap your betta will harass the shrimp . I still have a few shrimp in my tank with my betta and he will nip at them and chase them. They will stress the shrimp out and can cause death.
SO I say NO don't do it. Blue tiger shrimp are not worth losing besides you need to get more then one. You could try cherry shrimp they are hardy and cheap.
I had normal Tiger shrimp I could not afford the blues. the normals are so cool they come in all kinds of shades.
Here is a female of mine. She was a super tiger. She has eggs in this photo.