They don't always have all the sponsorships lined up when the teams launch the cars, though by the end of the first 3 races there usually is more space taken up by secondary sponsors.
A little different, but remember when Honda left and the team became Brawn, they had no sponsors (except maybe Virgin?) but once they started winning, the car had a lot more stickers on it.
McLaren began the season without a title sponsor in 2014 or 2015, whichever year they started the brief black and red/orange color scheme.
Side note: McLaren used to be my team but my inner fan has gone into hiding. I don't expect them to re-ascend from the back of the grid this year, but please don't make me wait another 6 years for me to see a McLaren win a GP.