Yes, unless the spoke tension is *far* too low or the rider is *far* too heavy... 😉
Each spoke has typically 100kg or so of tension, which is why they go "ping".
Assume a wheel has 32 spokes, and to simplify things split them into 8 "top", 16 "side", and 8 "bottom".
With no rider on the bike, all the spokes have 100kg of tension in them, which is what keeps the wheel rigid.
Even with a 400kg rider (!!!) over one wheel the top spoke tension would only increase by 25kg/spoke to 125kg/spoke (200kg "pulling up") and the bottom spoke tension would decrease by 25kg/spoke to 75kg/spoke (200kg less "pulling down").