Legit answer is
50% Maybe
50% Nope

Coming for Pilot training and getting a job are completely two different ways in the state of law US.
For example, Once you come for Pilot training usually with a M1 visa the state of entry in the US Immigration is recorded as STUDENT. ( you can't work period) until you have obtained a F1 visa ( Double Expensive College degree+Flight Training costs ) which gives you a cushion to work known as OPT.

Once you wrap your Pilot training and you want to stay then you need to acquire legal status to work lawfully in the states by getting sponsored or enrolling in a STEM degree program or getting a lawful marriage or parent sponsorship ( if they are US citizens) or talk to US immigration attorney.

The debate on this topic is very hot, especially among Indian students. mostly Excited & motivated folks
A very crucial note is it's all a lengthy process time-consuming and money-investing ways remember you just spend cr. for training you don't wanna waste time. Also if there is a will there is a way

New in AV Bazaar;
Some Dalaas of Dwarka and US Flight Schools are luring students to be an instructor- I call it a modern SCAM
For sure, the CFI (Instructor) JOB is very trending and it attracts newbie Pilots, but it's not as real as you might think.
Some instructor in the States works for free I mean Free.. free. (it's not work it's legal minimum wage time building)

You can always get an Instructor license but "YOU CAN NOT WORK"- Most of the time the flight schools you are enrolled in will not even gonna accept you as an Instructor- Since you don't have a legal work permit
"So be careful"

Welcome to Aviation, always have backups of the backup plans