It really shouldn't. Just try to avoid putting the nose so far down that you feel that you are sliding forward and have to hold yourself up with your arms, because that will lead to pain in your neck, shoulders, elbows, hands, etc.

Before you change saddles, measure everything. Your new saddle may be a different thickness and may have a longer nose or different rails so that you will have to change your seatpost and saddle fore/aft position to accommodate the differences. Measure the height from your cranks to the top of the saddle. Measure the distance from all parts of the saddle to the bars. That will give you a good starting point. Then get out and play around with it on your ride. Some saddles will flex more than others which may mean you'll need to do a little more tweaking based on feel. If you feel like you're bouncing off the saddle on the downstroke, you need to raise it up. If you feel like you're rocking or swaying against the sides of the saddle, you'll put it down.

You may also want to note where your knee is relative to the pedal spindle when your leg is at the 3 o'clock position. Generally, a fitter will put you where a plumb bob from the kneecap is even with the spindle, but your fit may ultimately have been different for several reasons. So make note of that too and double check your fore/aft with the new saddle after you set it up where the measurements to the bars are the same as what you had before. That will help account for any changes in WHERE you sit on the new saddle because of its different shape.