The short answer is NO. A background check will reveal your record. If this case is pending then it is not on your record at this time. A follow up check somewhere down the road will likely change your situation if you plead or are found guilty of the felony. I would be cautious about the manner in which you resolve these matters. It doesn't sound as though you have a previous record. If that's the case, there are numerous programs for first time offenders that result in the case being dismissed including numerous felony charges. Consult counsel and explain your situation. You maybe able to avoid a conviction altogether which would obviously alleviate your concerns about your employer uncovering your record.
The Connecticut Judicial Branch has a website available to the public that enables a user to search for a person's criminal history. The user can search for both convictions and pending charges. If you go to the site and follow the link through case look-up you will be able to enter your name into the search engine to determine whether you are in the system.
It depends upon the nature and extent of the background check being done. If the check only searches for felony convictions, and you do not have any, then your pending felony charge would not show up. However, it has become easier for background checking agencies to search more thoroughly. For instance, if someone were simply to check the Connecticut Judicial website and search your name in the pending cases section, that person could see your pending felony charge, your next court date, where the case is pending, and other information.