No. (If it did, it would only be very temporary. Saliva that comes in direct contact with said food may change pH for a very short period of time, until it reaches your stomach.) Your saliva is constantly being replaced by salivary glands in your mouth. There is a crucial flaw to the answer above. Yes, we are what we eat, but not in that sense.

Our bodies constantly go through homeostasis, which is a process that stabilizes our internal environment in response to the external environment. In order for your body to function properly, it needs it's enzymes to be at the top of their game. Anything other than an optimum pH makes them less effective and slows everything way down. That would be a huge problem. So, when food is ingested your body immediately works to bring the pH to an appropriate level. (The optimum pH is different for different regions of your body.) So while we are what we eat in the sense that we break down and reuse the atoms/molecules that make up food, our bodies do not change pH in response to food.

Saliva is produced by our bodies, so the replenished saliva that did not come in contact with the food would be at a normal pH. So I believe no it doesn't change.
Yes it has the role to play . if you eat something related to acids such as vinegar containing acetic acid. in tamarinds tartaric acid etc ...can decrease the ph value making the mouth acidic which can decay the tooth enamel. and if you consume deepfried potato chips or pakras made by bakingsoda (besan) can increase the ph value of your mouth indicating alkaline and basic medium thus different types of food play an imp role on our mouths ph. saliva itself shows ph value 7.4 that is slghtly higher than neutral medium .the main role of salivary amilase is to break down the carbohydrates to maltose and sucrose and it softens the food to be easily passed through oesophagus.