Inside each phone is a 2 user switch (or possibly a hub) connecting the computer to the phone then the phone to the rest of the network will add one more “hop” that the computer is away from you network backbone. This might add a very small delay in moving data around your network. Of course if you have to run an addition cat 5e line for each phone you are looking at an expense of wire and install time. Initially you might want to connect the phone to the network, then the computer to the phone, this will allow you to use the already existing wiring and get you phones up and running. After creating a baseline for throughput and network speed, run a few lines directly from the computers to the network and see if there is any kind of speed/reliability gain that would justify running separate lines to other system. It is important to get the network base line FIRST, then make your changes, that way you have real data to base your decision on.
The delay isn’t going to be a factor. Switching is fast, very fast, and the introduction of hardware switching in this manner is not going to impact data traffic latency. You should verify maximum throughput through the IP phone switch though. If you don’t get the bandwidth you expect that will impact your traffic.
Along with cabling costs, QoS is a factor to consider. Some manufacturers have synergies between IP phones and switch hardware which simplify QoS configurations. QoS is of course important because it enables you to prioritize your voice traffic over data which is essential to eliminating the latency, jitter and packet loss which severely degrades voice quality. Whether you connect your PC to the IP phone switch or directly to your access switch will impact how QoS is deployed.
Take a look at my blog entry on VOIP. This may help you gain some understanding of this network configuration. Networks today have not gotten simpler to manage. They have only become more complex and things like VOIP contributes to that complexity. There is no worries about having a computer downstream from a phone. The main concern would be the power needs of the phone device. Most phones get power from the ethernet drop so your switches will need to be able to provide enough power to the phones. The other option is a power brick for the phones or softphones on the computer (which in my mind causes high complexity issues with firewall configuration). Note that POE switches may not support a full load of phones. In other words, a 48 port POE switch may not be able to support phones on all 48 phones due to power consumption levels.
So, as you see, there is a lot to consider in your implementation. You should have a good implementation partner for this event if you have never done this before.