The answer is yes. The God of the OT approves of polygamy.
Proof of this can be found in Deut. 21:15
If a man has two wives, and he loves one but not the other, and both
bear him sons but the firstborn is the son of the wife he does not
The bible here states dryly the firstborn law in regards to someone that has two wives, it does not seem to condemn this act at all.
In Deut 17:17 the king is instructed not to take many wives, but he is surely allowed to take more than one (According to the Jewish Rabbis the limit is 18, which is exactly what David had. see this question ).
I post here a possible explanation as to why god may have allowed polygamy in ancient times.
First, while there are slightly more male babies than female babies,
due to women having longer lifespans, there have always been more
women in the world than men. Current statistics show that
approximately 50.5 percent of the world population are women. Assuming
the same percentages in ancient times, and multiplied by millions of
people, there would be tens of thousands more women than men. Second,
warfare in ancient times was especially brutal, with an incredibly
high rate of fatality. This would have resulted in an even greater
percentage of women to men. Third, due to patriarchal societies, it
was nearly impossible for an unmarried woman to provide for herself.
Women were often uneducated and untrained. Women relied on their
fathers, brothers, and husbands for provision and protection.
Unmarried women were often subjected to prostitution and slavery. The
significant difference between the number of women and men would have
left many, many women in an undesirable situation.
So, it seems that God may have allowed polygamy to protect and provide
for the women who could not find a husband otherwise. A man would take
multiple wives and serve as the provider and protector of all of them.
While definitely not ideal, living in a polygamist household was far
better than the alternatives: prostitution, slavery, or starvation.