Well, no. 1) That term already has a definition for something else. 2) Gold isn't the metal most associated with emotions.
That would be copper digger. Now we have a new term for a very common issue.
Though I should point out, it's not about crotch shape. My male partner does 90% of the emotional labor in our household, because I suck at it and we want it to get done right. Conversely I do 100% of pest control. Other responsibilities are divided based on interest and ability.
Now, if one partner wants to marry into money and is willing to offer emotional labor, while the other has money and wishes to procure emotional labor, they may be quite happy with each other. This arrangement is popular in many societies; so long as it is equitable and both partners are pleased with the deal, all is well. Not good is when one person gives much more than the other, regardless of who is mooching what. Healthy relationships are balanced.
Where did "gold digger" come from anyway? It's a term for a woman who has the self-respect to demand payment for her hard work, and that usually is emotional labor (sometimes also sex). She's not giving it away for free, and that irritates people who expect to get it for free.