Speak to your psychiatriast about finding a mood stabilizer that won't cause cognitive blunting or make you feel slowed down. The more time you are off one, the more likely moodswings are likely to return. Its not a good idea. There are an increasing number of options and they shouldn't affect your ability to be in a marathon or anything else for that matter.
your question resembles the situation where one asks: can I have children without getting married. The answer is : I tried and it worked.
The reason why people get married to get children is that the children can grow in a healthy environment. Unmarried couples usually separate so are the married ones but with less probability.
So can you not take mood stabilizers. It might work for some time, but in the majority of the cases, it's risky, because this illness has hidden hazard with plenty of pitfalls and can get worse.
good luck in either situations