Probably yes.
We’ve had a similar discussion some while ago and fixing the seed in such a setup to get the same initializations might be a bit tricky.
You could instead use the state_dict of one model to set all parameters of the other.
Since you are using dropout in your model, you would have to set the seed additionally.
Here is a small example using your model definition:
class NetA(nn.Module):
    def __init__(self):
        super(NetA, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv2_drop = nn.Dropout2d()
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)

    def forward(self, x):
        x = F.relu(F.max_pool2d(self.conv1(x), 2))
        x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
        x = x.view(-1, 320)
        x = F.relu(self.fc1(x))
        x = F.dropout(x, training=self.training)
        x = self.fc2(x)
        return F.log_softmax(x, dim=1)

class NetB(nn.Module):
    def __init__(self):
        super(NetB, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv3 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv2_drop = nn.Dropout2d()
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)
        
    def forward(self, x):
        x = F.relu(F.max_pool2d(self.conv1(x), 2))
        x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
        x = x.view(-1, 320)
        x = F.relu(self.fc1(x))
        x = F.dropout(x, training=self.training)
        x = self.fc2(x)
        return F.log_softmax(x, dim=1)

modelA = NetA()
modelB = NetB()
modelB.load_state_dict(modelA.state_dict(), strict=False)

# check some params
print((modelA.conv1.weight==modelB.conv1.weight).all())
print((modelA.conv2.weight==modelB.conv2.weight).all())
print((modelA.fc1.weight==modelB.fc1.weight).all())

x = torch.randn(1, 1, 28, 28)
torch.manual_seed(2809)
outputA = modelA(x)
torch.manual_seed(2809)
outputB = modelB(x)
print(outputA==outputB)
> tensor([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], dtype=torch.uint8)