The phrase "allegedly engaged" is correct and usable in written English.
It can be used when discussing claims or accusations that someone is involved in a particular activity or situation, without asserting that it is definitively true.
Example: "The politician was allegedly engaged in unethical practices during the campaign."
Alternatives: "reportedly involved" or "supposedly participating".
The two allegedly engaged in a physical altercation.
Past targets have included America, Ukraine, and foreign do-gooders allegedly engaged in espionage.
"Yield burning is a serious matter allegedly engaged in by sophisticated companies that should know better".
But that hardly puts him in the backseat of the car where Flowers was filmed allegedly engaged in mergers and acquisitions of a more physical kind.
It was during the Miss Universe competition, in November of 2013, according to the Steele dossier's sources, that Trump allegedly engaged the prostitutes at the Ritz-Carlton.
It allegedly engaged in tactics to persuade its staff not to vote in favour of joining the strong New York union, the Hotel Trades Council (HTC).
Some Latvian banks have faced international criticism for allegedly engaging in money laundering.
They were not involved in organizing the parties, the State Police said, but were suspended for "allegedly engaging in misconduct".
On March 29th the SEC brought civil charges against Cheng Yi Liang, a chemist at America's Food and Drug Administration FDAA), for allegedly engaging in a $3.6m insider-trading scheme.
In Beijing the state-owned media reported last week that Zhou Liangluo, the chief of Haidian district, home to many of the city's universities and high-tech companies, had been detained for allegedly engaging in shady property deals.
In reality, Cruz's campaign has been repeatedly hit by rivals for allegedly engaging in dirty tricks, and both Trump and Rubio have openly called the Texas senator "a liar".
