No it doesn't work that way with taxes. Here's an example with tax brackets for head of household filing:
10% Over $0
12% Over $13,600
22% Over $51,800
24% Over $82,500
32% Over $157,500
35% Over $200,000
37% Over $500,000

So for example - if you make a taxable income of 51,800 you pay 10% tax on the first 13,600, 12% tax on the amount between 13,600 and 51,800. If you received $20,000 in alimony on top of your income, you would pay 22% taxes JUST ON THE ALIMONY, while still paying your previous tax rate on your own earned income. Get it?