Nope, it won't affect your strength gains. I would personally do a brisk walk over jogging. Doing something like a brisk walk 30 min 3- 5 times the week can positively affect barbell training (provided you don't overdo it). Just start with 3 x week and see how that works. If you see your training being affected, then lower the number of days, speed of walk or minutes. If not, then increase those variables till you find a balance.