The 22-year-old was due to arrive at Manchester’s AO Arena on Tuesday afternoon, four days after his defeat by Jannik Sinner in the semi-finals of the US Open.
Draper struggled physically during the encounter, with anxiety and the humid conditions causing him to vomit several times on court.
But British captain Smith reported the British number one is in good health, with a decision to be made on his involvement following practice.
“Until we get on the court and start doing some stuff, it’s quite hard to tell how (he) feels,” said Smith.
“It’s just a question of figuring out where he is at with his energy, how much tennis he can play over the course of the week. But, if he’s good to go, he’s good to go. If he’s not, I’ve got every faith in those sitting beside me now.”
Britain will take on Finland, Argentina and Canada over the next five days in Group D of the initial stage of the Davis Cup Finals, with the top two teams progressing to the last eight in Malaga in November.
Draper’s presence is crucial for the home nation, who are looking for a new talisman now Andy Murray has retired, while Cameron Norrie is also missing as he continues to be troubled by a forearm injury.
“We are absolutely thrilled that he’s coming,” Smith said of Draper, who made his Davis Cup debut at the same venue last year.
“You can tell straight away that he gets Davis Cup. He plays with passion, pride, fight, and you mix that with the fact he’s a top-20 player with unbelievable quality, he’s going to be a very important member of the team not just this week but for many, many, many years to come.
“He absolutely loves it and his commitment by coming here just shows that.
“Obviously we miss Andy being around, just in general. He was a bedrock of the team for the last couple of decades, even put his heart and soul into one of the rubbers here last year against Switzerland.
“You could still see how much it meant to him then. But he’s not forgotten is he? He’s left a massive imprint and legacy on definitely me but also all the guys that are sitting here.”
Draper is joined in the team by veteran Dan Evans, doubles specialist Neal Skupski and two debutants in Billy Harris and Henry Patten.
Harris, who famously spent the early part of his career living in a converted transit van while touring around Europe, has achieved another first at the age of 29 while Patten, 28, has been rewarded for his surprise Wimbledon title in men’s doubles.
Britain will be favourites to beat Finland whether or not Draper plays but Argentina boast impressive strength in depth and Canada have star duo Denis Shapovalov and Felix Auger-Aliassime in their line-up.
Manchester, we’re ready ✨🎾
The Lexus GB @DavisCup Team are set at the @AOArena pic.twitter.com/NiFBTJKAQW
— LTA (@the_LTA) September 10, 2024
Last year, Britain pulled off one of the most dramatic victories in the history of the competition when Evans and Skupski prevailed in a final set tie-break against France in the deciding doubles rubber to book their spot in Malaga.
Smith is expecting another nail-biting week, saying: “I think it’s a really even group, and something always happens. That’s what Davis Cup is, players take their chances.
“But I really believe we can be successful here. We’re really determined to do that. All the players here are in good confidence, playing well, so why not? We’ve got to get after this.”
Smith will certainly be glad Britain are not in Group B, which features Australia, Czech Republic, France and hosts Spain, who are led by Carlos Alcaraz.
Defending champions Italy, who are without Sinner, are taking on the Netherlands, Belgium and Brazil in Bologna, while the USA, Germany, Slovakia and Chile are doing battle in Zhuhai.
