The Sunderland right-back was a late call-up to the squad, which jetted out to Prague this afternoon ahead of Friday's clash.
His inclusion will provide cover for Alan Hutton, who is struggling with a groin strain, and that means Bardsley could make his debut sooner than anticipated.
Asked if he would be happy for the former Rangers and Manchester United player to start the match, Levein said: "If the situation means that Phil has to play, then yes.
"He played last week against Manchester United for Sunderland. He's an experienced enough player and I don't have any qualms about that at all."
Bardsley, 25, was born in England but qualifies through his Glaswegian father and had a change of heart about representing Scotland after dismissing the idea as an 18-year-old.
"It's been a bit rushed to be honest," said Levein. "We have been aware of Phil's eligibility for a while, it was just a matter of finding out if he was going to commit to playing for Scotland.
"We chased it up and found out that he had a change of heart from a couple of years ago and he's desperate to be involved.
"We tried to progress things as quickly as possible and everything has been done. He's another experienced but young player who fits into the profile.
"I'm really pleased to have him on board. He's playing every week in the Premiership, which is a big plus for us."
Levein rated Hutton's chances as "pretty good", adding: "He did a little today and felt better than he did yesterday. He maybe has an 80% chance but I'm guessing.
"I see a general improvement on the injury and the amount of positive feedback I'm getting."
Levein is also hopeful goalkeeper Allan McGregor will prove his fitness ahead of the match.
He said: "He's fairly positive. He did a little bit today, not a full session. He's had a recurring thigh strain which he's played with.
"He played three games last week for Rangers carrying this injury.
"He has had a full week's rest this week so I would expect him to be far better come Friday night than he was when he played against Hearts.
"I'm hopeful but I'm not going to take any chances with anybody. If he's fit he'll play, if he's not he won't."
The Scotland boss added: "We have some issues that I'm hoping will be clearer in training tomorrow evening.
"There are a couple of guys who haven't done a full training session as yet but I'm hopeful those guys will be okay and available for selection."
However, Levein refused to be drawn on speculation that Kenny Miller will be dropped on Friday night, with the Rangers striker hoping to earn his 50th cap.
"The team will be named as usual 24 hours before the match," said the manager.
"I'm not going to make any comments at this moment in time about who's playing and who's not.
"The team hasn't been named, I can assure you of that. I'm not going to give any indication as to what the team is at this moment in time."
Asked if Miller was still in his thoughts, he replied: "Of course."