Apparently, according to most authorities, no. In fact, at least one great Rabbi (Rabbi Yehiel Yaakov Weinberg in Seridei Eish) says the conversion cannot happen under any circumstances, in order to prevent the man from risking the procedure. Pikuach nefesh in an unusual application, I suppose.
Sorry, hemophiliacs. Rabbi Abraham Isaac Kook (the first Askenazi Chief Rabbi of Israel) says no in Da'at Kohein. In Rabbi Weinberg's case, he refused an admittedly "pure and selfless" conversion of a man suffering from diabetes and a heart condition. Because of these conditions, the doctors felt that he could not safely have the procedure.
Here's the reasoning: circumcision is absolutely required by the halacha. An uncircumcised Jew is punished with being cut off from his people, so every day he remained uncircumcised, he is actively breaking the halacha. Further, he states a policy reason: Rav Kook says that this would create an "ambiguous situation" that might confuse people as to the requirements for a proper conversion or think they can opt out of it based solely on a doctor's recommendation. Very interesting stuff...
I'm curious if any of you know how this applies to a born Jew, either a baby or an uncircumcised adult baal teshuva. It seems that pikuach nefesh would require forgoing the circumcision on a baby, and it is definitely acceptable to delay the circumcision of a baby, per the recommendation of a doctor and your rabbi. If the child were a hemophiliac, could he ever be required to get circumcised? If not, is there still a punishment for not being circumcised?
Who says reading halachic opinions is boring??