Absolutely not. I'm too much of an individualist to want to be merged or diluted by another personality.
I'm tempted to beam this to the DS9 Forum, but I think you want this conversation will be more about identity and individuality than the show, so I'll leave it here.
The intriguing thing about the joining is that each host personality is still retained and they still can maintain their individualism while sharing their body and minds with the symbionts. I don't think it dilutes your individualism, but enhances it. The host realizes their own uniqueness in their personality and also what they share in common from the most unlikely of people: gymnasts, diplomats and murderers.
In the episode where Jadzia was going through the ceremony where the rest of the crew took on the memories of the other hosts illustrates this pretty well. They were all different -- Curzon didn't want to go back "in." A decision brought about because his stubborn nature. When the Dax symbiote was stolen from Jadzia by Verad -- the symbiote felt an urge to continue Verad's morally bankrupt plan, despite the strong feelings of friendship towards the Sisko and the rest of the DS9 crew. The strands of individualism persists through all the hosts. Also, you also get to see situations from another viewpoint, and maybe realize things you never thought of. Spurring you to find new interests (Jadzia's interest in all thing Klingons, if I remember, was partly due to Curzon's involvement) and bring new perspectives.
I don't think your individualism would be diluted, but the joining would bring you a breadth of experiences you could draw on. You aren't dominated by the past hosts decisions, but you'll pick up things as well. Also, I believe a requirement (or, it was implied) is that the potential host has an established identity and strong sense of self. I'd apply to be joined. The whole concept is intriguing: the idea of viewing life from a different angle, different experiences, with the ability to make your own decisions.
edit: Just to add, we gave my dog the middle name "Dax", so if I got the dax symbiont, I could finally figure out what the hell dogs think about.
-nobody