I'm not 100% but here's my humble opinion.
Usually, each "visa" is an entity in itself even year to year. Getting branded as an expert is a must. But it's much easier to be labeled an English teacher since you are a foreigner. I presume you from one of the Big 6 (Canada, US, UK, Ireland, Australia and New Zealand). Even if you are not, it's still pretty easy and more academic as you go to smaller cities.
Without knowing the company nor the city, it is a little difficult to give you better information. Rules change from place to place (sometimes day to day). You don't have to give us the name of the company, but some details help; are they 100% Chinese owned, a State Owned Business, is their head office in your country of birth or another, how big or prominent are they here, are you their first, etc.
For example if you are American and you are going to work for Coca-Cola China, then getting labeled as a marketing Manager is a piece of cake.
To further answer, I don't think it will impact on you future Foreign Export Certificate since this needs to be renewd each year. Whatever your new company is will process this for you