That depends on the situation. Yes, if it was something like "Hey, I know you have this huge project deadline that I am a critical part of, and if you don't pay me a grossly large amount more, I am out" That is hostage taking, and they would not look fondly on you.
But the request of asking for a rate that you are being offered on the open market is not. They have 2 choices there: They can pay you more because you are worth it, or they can wish you the best. If this company had a bunch of employees come in and get take 30% comp less than you and did the same quality of work, do you think they would be "loyal" to you and grossly overpay you? Absolutely not, and they shouldn't. Of course, the company would love to just pay you less, but they realize that your value proposition still exceeds that.
Corporations are completely tone deaf. The way you say things and the details of your situations will not be perceived by the relevant decision managers.
In a small company, it can make a difference. In a large one, it won't.
But the request of asking for a rate that you are being offered on the open market is not. They have 2 choices there: They can pay you more because you are worth it, or they can wish you the best. If this company had a bunch of employees come in and get take 30% comp less than you and did the same quality of work, do you think they would be "loyal" to you and grossly overpay you? Absolutely not, and they shouldn't. Of course, the company would love to just pay you less, but they realize that your value proposition still exceeds that.