You and your sweetheart will absolutely be welcomed at the church. We don't turn anyone away. Now, I'm not quite sure what you mean by "acknowledge". You certainly won't be shunned or anything like that. Your local community will be happy to have you in their midst. 
If you and your girlfriend are looking at getting baptised into the church, however, you may have to make some changes depending on what you mean by "been with". In order to be baptized, a person must show that they have a desire to repent of their sins and keep the commandments. One of the big commandments is the law of chastity in that men and women should only have sexual relations with their legally wedded spouse. That would mean that you and your girlfriend would either need to commit to refraining from any sexual activity before marriage or take the plunge and get married. 
Regardless of your decision, just know that living the law of chastity, whether you are a member of the LDS church or not, brings tremendous blessings into your life, both before and after marriage. When we keep ourselves sexually pure, the Spirit of the Lord is able to more freely dwell with us and we are able to feel much closer to God.

Art hit the majority of the Law of Chasity.  
 
First let me congratulate you on your decision to attend services and potentially investigate the Church of Jesus Christ of Latter-day Saints. 
 
The Law of Chastity also applies to cohabitation before marriage, if you happen to be living with your girlfriend at this time you would have to live in separate places or be married before you could be baptized. If this doesn't apply then your all set.