Unclear, but probably not--it's a bit chicken and egg.

For example, we know that exercise can induce fat browning and enhance thermogenesis in brown/beige fat--a sedentary lifetstyle, the opposite. Exercising muscles secrete several different substances that increase fat browning.

Insulin resistance and high blood glucose probably also inhibit fat browning. Recently, a new type 2 diabetes drug that lowers blood sugar by making you pee more of it out was found to increase fat energy expenditure. So eating a lot of sugar (especially in combination with a vitamin-poor diet, which tends to enhance insulin resistance on a high-fat, high-sugar diet in mice) probably decrease thermogenesis.

The thermogenic capacity of adipose tissue also has a circadian rhythm. Circadian rhythms are not just driven by light, but by when you eat. If you eat throughout the day and night, rather than restricting your food intake to 12 hour or smaller intervals, you can mess with your clock and you are also more likely to be obese--in mice, this actually happens regardless of the quantity of food intake, though I am not sure if there are human studies showing that.

Inflammatory signalling suppresses fat browning, and inflammation in adipose tissue is highly associated with obesity and insulin resistance.

There's also a transcriptional repressor of fat browning and thermogenesis which is upregulated by estrogens, which are at higher levels in obese people, including men.

Poor diet, lack of exercise, eating frequently, and obesity are a perfect storm of factors to turn off fat browning and thermogenesis.

So it's more likely to be an effect than a cause, but once things get rolling, the door is certainly open for it to be a continuing contributing factor.