Very initial reactions to RADA (Rodchenkov Anti Doping Act). Not extended analysis and just my own opinions.
When I first read the posts about this law extending to overseas events, I thought, nah, can't be, exaggerated. Well butter me up and call me a biscuit.

It does.
1. The first person ever charged under RADA (in January) resides in the US, but allegedly doped non US athletes at non US comps:
The law targets people who would skirt doping regulations in international competitions, but it does not apply to major American leagues like the N.F.L. and Major League Baseball.
www.nytimes.com
www.justice.gov
2. RADA prohibits any person, other than an athlete, to knowingly carry into effect, attempt to carry into effect, or conspire with any other person to carry into effect a scheme in commerce to influence by use of a prohibited substance or prohibited method any major international sports competition. 21 U.S.C. § 2402(a).
There is
extraterritorial Federal jurisdiction over an offense under this section. 21 USC § 2402 (b). That means, the US considers it a crime prosecutable in the US, even if it didn't happen in the US.
www.law.cornell.edu
3. One law firm's analysis of the Act:
On 4 December 2020 the much publicised Rodchenkov Anti-Doping Act 2019 (“the Act”) was signed into United States law. The Act is designed to assist the ...
mse.dlapiper.com
TL; DR:
The Act does allow for prosecution of "doping" violations in the US that occurred outside the US if they affected US athletes. The Act allows harm to other parties such as broadcasters to be taken into account.
Recognition and enforcement of arrest warrants in other countries is a whole separate area of law. Needless to say, should an indictment or warrant even happen, I would never expect Russia to honor it. I wouldn't expect the US to try.
Most serious hypothetical outcome: WADA sustains a violation. Proof is adduced that someone else gave the athlete the banned substance. Warrants are issued for those persons.
Do they ever set foot in the US again?
This is not saying what
will happen, this is saying what
could.