No. Equity removed from a home in a cashout transaction is never taxed.
However, if when you go to sell the home, if you are then subject to capital gains, hopefully you haven't already spent it. But that's unlikely to be an issue, as the first $500,000 in gains is tax-free for a married couple who have lived in the home as their primary residence for at least 2 of the prior 5 years.
And considering that most of that money will actually go to capital improvements to the home, you'll be increasing the cost basis of the home, limiting the actual gain when you do sell. Just be sure to keep your records of the improvements until you sell! I don't know what counts as a capital improvement and what doesn't, but when the time comes, a CPA will be able to answer those questions for you.
10 years in mortgage banking