It's not allowed.
You cannot use this emergency rule to buy a house. It's not "a COVID-19 related purpose", as stated in your quote in your question.
The way tax regulation works is a) Congress passes laws, and b) IRS interprets the laws into regulations. Quick googling shows the law is passed but the regulations are not written yet. So you will be at the mercy of IRS's regulations, and that's no place to be.
Here's what one senator is saying. You have to have adverse financial consequences of some kind:
- You, your spouse, or dependent has been diagnosed with the coronavirus (i.e., SARS-CoV-2 or COVID-19),
- You have experienced adverse financial consequences because you have been quarantined, furloughed, laid off, or have had work hours reduced due to the coronavirus,
- You are unable to work because of a lack of child care due to the coronavirus,
- You own or operate a business and have had to close or reduce hours due to the coronavirus, or
- You have experienced an adverse financial consequence due to other factors as provided in guidance issued by the Internal Revenue Service.
IRS regulations will certainly flow from that. So you will find in 2021 when filling out your taxes, that you cannot tick any of the boxes, and thus your $100k distribution is treated as a regular distribution with 10% penalty and full taxes due on April 15 2021, and cannot be restored back into the 401K.
Other than that, this is a very robust 401K quasi-loan
The biggest worry when withdrawing from a 401K in a crisis is the contribution can never be replaced; thus you'd damage your savings and impoverish yourself in retirement. However, they wisely addressed this issue. If you qualify for this emergency withdrawal, you are allowed to put the money back in in the next 3 years, i.e. make an excess make-up contribution.
They are waiving the 10% for qualified withdrawals, and the income tax from a Traditional distribution will be spread over the next 3 years. You do need to pay tax on the distribution, but you are also allowed -- encouraged -- to "put the money back" as an excess contribution (beyond your normal annual $19,500 allowance, say). When you put the money back, you get the normal tax deferral, which cancels out the taxes due.
Say you take out $90,000 out of a Traditional due to a genuine crisis. Hospital bills or you will lose your house due to unemployment. You then pay taxes on $30,000 of it in 2021, 2022 and 2023. However you "put the money back", contributing $30,000 (beyond your normal $19,500) into the traditional in each year. That $30,000 re-contrib is a legit 401K contrib, and as such, has its taxes deferred. That deferral cancels out the taxes coming due.
And neat as a button, you are back to status quo ante. You got to "borrow" the money for 1-3 years, you put it back in good order, your net taxes are zero, and the money in your retirement account is fully restored (as far as the IRS is concerned. The market may have other ideas.)
It's a really brilliant scheme, I can't believe they came up with it in 2 weeks.
Wait wait wait. You just want to change to Roth!??
One of your ideas was to invest in a Roth IRA. Good idea, wrong method!
You can already convert your 401K to a Roth 401K. You can just pick up the phone and do it. There are no contrib limits, the only thing that limits you is the tax bracket you're willing to throw yourself into by doing so (and no offense I have a feeling this is all news to you; educate yourself a lot before doing anything big).
Now if your company doesn't offer Roth 401K, get with HR and tell them to get on the ball. Most companies now allow this.
Withdrawing from a 401K using this program to contrib to a Roth, would be a huge mistake full of disadvantages and lacking any advantages. Right off the bat, your contrib would be limited to $6000/year. 401Ks are absolutely protected from attachments, lawsuits and bankruptcy. IRAs, that protection varies by state and is sometimes nonexistent.