Long term, yes it would and during high CPU usage if there's no fans to carry the heat away the CPU may overheat.
Also they do make fanless PSU's but of course, there not very safe left on 24/7.
Which i3 are you going for...
Try and get one with as low TDP as you can (which is the maximum heat the CPU kicks out)
Then we may be able to reduce the amount of fans needed dramatically