I exercised throughout my twin pregnancy (albeit w/ significantly less exertion as I got into the third trimester.)
I routinely had a higher BP from the pregnancy itself but the only time that was an issue was in a hot dressing room trying on bras for breastfeeding!
The exercise was important for me mentally, and I think also REALLY helped me physically w/ carrying the twins and recovering easily from the c-section.
I'm not an athlete, I'm fairly overweight, and middle-aged, but it still really helped.
Good luck OP.