I'm with Hk328 on thinking that these deferments are for very special circumstances (and most likely relationships are not one of them, sry). Since this is something that they expect applicants to have in mind (family distance, relationships, etc), I don't believe a committee will give defer on such grounds, so ultimately it is up to you to decide.
There are some questions that you may ask yourself to find out where your feelings and motivation are (at least I considered these before making a decision):
- if suddenly you find yourself without your partner after rejecting an offer (for any reason), do you think you would be happy with your decision?
- is the presence of your partner essential for you to succeed in your studies? usually, the first years are brutal and you don't have much time anyway
- do you think s/he would do the same for you?
- if you are rejected for asking a deferral, how do you think you would feel?
- if you receive an offer and not get the deferral, decide to maintain your relationship and reject the offer, but next year you don't get an offer and your partner gets one, how do you think you would feel?
- if you don't apply (or enter) now, what are your plans to still be competitive for the next applications round?
- If ten years from now you are either 1) with this partner but without dream degree OR 2) with dream degree but without this partner, which one would you choose?
Don't need to answer here, those are just to help you to think about the situation.