They will just not be updated. The running stats are already stored in bn.running_mean and bn.running_var. If you set this layer to eval, the running stats will just be applied withour updating them. Have a look at this small example:
bn = nn.BatchNorm2d(3)
x = torch.randn(10, 3, 24, 24)

# Print initial stats
print(bn.running_mean, bn.running_var)

# Update once and print stats
output = bn(x)
print(bn.running_mean, bn.running_var)

# Set to eval; the stats should stay the same
bn.eval()
output = bn(x)
print(bn.running_mean, bn.running_var)

# Set to train again; the stats should be changed now
bn.train()
output = bn(x)
print(bn.running_mean, bn.running_var)