The simple answer is no, if you're in any doubt as to whether you should take your boyfriend to the Christmas company party, then you leave him behind, especially if you are on the rocks.
Going to a party where you don't know anyone else, and you aren't on the best of terms with the one person you do know, is always awkward. Add in the mixture of alcohol, watching other couples have a good time and the high expectations people often have of
Christmas, you've got a recipe for potential disaster.
Imagine if the worst does happen, and you and your boyfriend have a blazing row at the company Christmas party. Your boss won't thank you for bringing personal issues to a work event, and your colleagues will feel uncomfortable. At best, the party will pass off without incident, and you and your boyfriend will be in the same sport with your relationship as before. You shouldn't look on a Christmas company party as the chance to 'make everything better' with your relationship.
Try and discuss the party beforehand with your boyfriend; he may resent having to tag along; he may dislike being left behind. Find out first! If a compromise is needed, perhaps he can turn up for the last hour or so of the party, or you could meet up afterwards for a drink.
A company Christmas party can be a minefield, even it it is meant for fun. In this YouTube film, Dr Sylvia Gearing advises on what to avoid: