Is it legal for a single woman to marry her gay male friend so he can have health insurance?

On one level state laws do not inquire nor do officials generally care about a couple's purpose in getting married, or whether one or both members of the couple are gay or straight. 

Whether one or both members of the couple are getting married for love, money, to legitimize children, to facilitate a future inheritance, to qualify for an inheritance, to enhance community status, to serve as a "beard," for religious reasons, for professional or political purposes, or to be able to extend health insurance or other benefits to the proposed spouse, a couple generally can get married. (In several states couples of the same gender also can marry. In some states a couple can also enter into a "civil union" as an alternative to marriage.)  

Once married, as far as the state goes, you'd be legally married. If the marriage takes place in state 1 that marriage would be recognized in all other 49 states and the District of Columbia under the "full faith and credit credit" clause of the U.S. Constitution (assuming it were between a man and a woman -- that limitation due to the "Defense of Marriage Act" -- which does not require other states to recognize same-sex marriages. Marriages conducted in foreign countries are generally not covered by full faith and credit.) 

Once you're legally married the only way out of the marriage would be by death, divorce or annulment. In other words, even if the marriage outlived its usefulness the couple would still be married, and it would be necessary to go through a divorce or annulment to get unmarried.

As a married couple if one of you meets someone and wants to get married, or you get into an argument, or your spouse does something that creates liability for you such that you find yourself liable for your spouse's debts, or you don't want to file joint tax returns and learn that the tax rates can be meaningfully higher when you are "married filing separately," or your spouse gets into something unseemly, or generates excessive publicity and that's not okay with you, or you find yourselves totally incompatible, you'd need a divorce or annulment. Further, in a divorce or annulment the court may award some of one spouse's property to the other and provide for alimony or maintenance.  

In the meanwhile, so long as you are married, in the event of the death of one spouse the other would have whatever the state provides by way of inheritance rights to the survivor. In addition, as a married couple you'd each potentially be liable to creditors for certain expenses and maintenance of the other, and banks might look at both spouses' credit ratings in granting loans or mortgages and require both spouses to sign. In short it may be a perfectly legal marriage, but produce a perfectly awful result. Further, the marriage may NOT always accomplish your immediate objective -- getting health insurance for your friend.

Although gay and straight couples have been getting married for years to benefit from affordable health insurance -- isn't it awful that people have to go to those lengths? -- the insurance company usually has no basis to know that it is a marriage of convenience. However, that does NOT mean that if the spouse benefitting from the insurance were to incur enormous medical bills the insurance company would not investigate and attempt to deny coverage on the basis that the marriage was a sham. (If it's group health innsurance, and the employer's costs were to increase materially due to the high claim generated by your spouse, the employer may also have standing to complain.) I can't give you a definitive answer as to whether or not your insurance company or employer would prevail in the unlikely went it claimed coverage should be denied due to fraud or sham, assuming it ever found out. I do understand that sham marriages are illegal for immigration purposes, and may even subject the couple to possible Federal criminal scrutiny and prosecution as immigration fraud.

In any event, it will be wise to consult with a family law attorney and probably to enter into a prenuptial agreement with your proposed spouse before getting married in circumstances such as you are suggesting.