The short answer to this question is: it depends if the rabbi of the Orthodox synagogue considers the conversion valid.
There are several requirements for a conversion to Judaism. They are mikvah (ritual immersion), brit milah or hatafat dam brit (circumcision or taking a ritual drop of blood from a circumcised male), and kabbalat ol malchut shamayim (acceptance of the yoke of the kingdom of heaven). Men are obligated to fulfill all three requirements and women, clearly, are exempt from brit milah or hatafat dam brit.
One of the biggest differences between an Orthodox standard of conversion and a Conservative one lies in the definition of kabbalat ol malchut shamayim. This concept means that the individual undergoing the conversion must spend a period of time studying the Jewish tradition and be prepared to take on the obligations and responsibilities of a committed Jewish lifestyle. But what exactly does that mean? Does the person have to pray three times a day, observe all of the Jewish holidays, observe all of the laws of Shabbat, and commit to keeping kosher to one specific standard? In short, what is the "check list" for determining whether or not one has "committed" themselves to an active Jewish lifestyle? What defines kabbalat ol malchut shamayim? This is the main question that may lead to a difference of opinion between a Conservative rabbi and an Orthodox rabbi on whether or not the conversion is valid.
Another difference of opinion about the conversion's validity may center around witnesses. The qualifications for who can be a witness to the mikvah, and who can sit on the rabbinical court might be different for an Orthodox or Conservative rabbi. The qualification of a witness (their level of observance, their gender) might call into question the validity of the conversion for the Orthodox rabbi. Additionally, as we are talking about an adult, there may be differences of opinion surrounding who is permitted to perform the circumcision (if needed). Does it have to be a mohel (one who does ritual circumcision), or can it be a doctor who is Jewish and well versed in the laws of ritual circumcision?
I would imagine that each of these questions (and perhaps a few others) would be important to the Othodox rabbi because he would have to determine whether or not the convert asking to be married was Jewish according to his understanding of Jewish law.
Needless to say, this is an extremely sensitive issue for all involved. A Conservative rabbi may have questions about a Reform conversion much as an Orthodox rabbi would have questions about a Conservative conversion, I understand the challenges of this issue. I would hope, however, that this decision would be handled with the utmost sensitivity, care, and with an eye towards striving to bring this couple closer to Judaism and a Jewish lifestyle -- something they clearly value. In a time where there are fewer couples who even think to ask to be married in a synagogue, all of us, regardless of denomination, should approach these tasks with integrity and sensitivity as we seek to bring Jews closer to their Judaism.