Possibly, but I think it's unlikely, except indirectly.
Exercise increases natural carnosine levels, so someone who both takes extra creatine and uses the energy to increase their exercise level probably would have increased carnosine. I don't know if creatine production is also increased in response to exercise.
The two molecules are derived from different amino acids so there is no competition in their production, and taking one won't provide raw materials to produce the other.
The two supplements work by independent mechanisms (more details below) so there is little reason to expect an increase in one compound to affect the level of the other. The only overlap between the two is that they both buffer pH (as do most peptides to some extent). If the body naturally produces extra carnosine in response to pH stress (and I don't know if it does), that effect might be reduced by the presence of creatine. In other words, creatine supplementation might actually reduce carnosine production. I'd guess such an effect would be small, and would be more than offset if the individual was doing extra exercise.
Creatine is converted within cells to creatine phosphate (CP), which is used as a short-term source of phosphate energy to regenerate ATP from ADP. The theory is that extra creatine leads to extra CP and hence more energy in the early part of exercise. Sure enough, studies have shown a benefit from creatine supplements for short, intense exercise. Creatine also acts as a pH buffer.
Carnosine is an antioxidant and buffer. A hard-working muscle cell has a decreased pH due to carbonic and lactic acids, and an increased concentration of reactive oxygen species from respiration. Carnosine would be expected to prevent damage from both of these sources, which may be (and apparently is) observed as a reduction in fatigue during exercise.