Most likely yes, you can fit that tube just fine.
The limit where you can no longer fit the inner tube to your tire is that the tube becomes wrinkled and you cannot remove those wrinkles no matter how hard you try.
Actually it's beneficial to use as big tube as you can fit there. If the tube doesn't stretch much, it probably is somewhat harder to puncture and also leaks naturally air less than a small and much-stretched tube, so you don't have to pump up the tire as often due to air leakage.
I have found that on my 622-28 (700 x 28 in other notation) Continental GP5000 tyres, I can fit a 32/47 tube just fine.
Note that occasionally, there's a trend that a manufacturer makes a 27mm tire and calls it 28mm. It reduces weight so everyone goes and buys that tire. Then another manufacturer goes in to the same game, making a 26mm tire and calling it 28mm. A third manufacturer then decides to call a 25mm tire a 28mm tire. The end result is that tires can be much narrower and lighter than what their specification says. More about that.
However, I don't believe the dishonest size labels are currently actively used so you can be reasonably certain that a 28mm tire in fact is a 28mm tire. Maybe it's 27mm, maybe 29mm, depending on the rim but it's intended to be 28mm.
Also an observation: if the tube you get is really 28-32C, that sounds too narrow a range. Schwalbe's 28mm tube doesn't fit just 28-32C, it fits 28-47C. This could be an indication that your tube is not from a reputable brand.
Furthermore, I heavily suggest you to patch punctured tubes instead of buying new ones. Tubes aren't single-use-only.