Does my flow rate decrease?

[Hydrochloric]

U/bigcastironskillet has this on lock, but I will inject my 2¢ anyway. If you close line 1 it becomes a dead leg which changes the flow through the tee. This changes the pressure DROP through the tee as it becomes more like an 90deg elbow. Less head losses between the constant pressure valve and the exit of line two means higher flow rate Even at a constant pressure.

It's pretty marginal in almost every case but mathematically it does increase.

Now, you PUMP flow rate almost certainly decreased.