Doing the math on that would mean it would take you 6000 hours to do it, meaning 250 days, meaning 8 months (using 30 days in a month), meaning that you would be spending at least 3/4 of a year making meth in a game.
From level 0 to 100, you need 23,336,413 EXP. A Proverkill Hoxton Breakout gives 1,056,000 EXP. So 23336413 / 1056000 = 22.09. You'd have to do that heist 22 times. It takes about 30 minutes to do both days of that heist. 22 * 0.5 = 11 Hours to about reach level 100.
March is in Double EXP month, so 5.5 hours to reach level 100.
Don't forget Infamy and Perk Deck multipliers, making that time
even shorter.
Sources:
http://payday.wikia.com/wiki/Heists_-_Rewards_%26_Contract_Prices,
http://payday.wikia.com/wiki/Reputation_%28Payday_2%29(Calculated with recent EXP dosage, too. This maths is of current time)
They did the mathEdit:
Oh and by the way, 5.5 * 20 = 110 Hours. A week has 168 hours. A average human sleeps 56 hours a week. So Espio's friend has 2 hours of leisure time in between sleep and playing Payday 2 non-stop to reach 19-100 in one week. (Dated in Double EXP March)
But of course the infamy bonus gives him even more leisure time.