Simple Explanation:
Your computer will be fine if you have multiple internet connections from multiple network adapters. So long as you aren't using both to connect to the same network, you should be fine.
Windows will automatically determine which internet connection to send traffic to, and will typically use that same connection so long as it's available. If you're only browsing the internet and not running a server or something, you shouldn't see any negative effects from the dual connections.
More Technical Explanation:
You can have multiple network connections active at the same time. The network connection that you use first is defined by the routing table. You can see this by opening a command prompt (cmd.exe) and running route print.
For example:
IPv4 Route Table =========================================================================== Active Routes: Network Destination Netmask Gateway Interface Metric 0.0.0.0 0.0.0.0 10.0.2.2 10.0.2.15 10 0.0.0.0 0.0.0.0 10.0.1.1 10.0.1.15 20 The first route will be used for your traffic to the internet (0.0.0.0/0) because the Metric is lower. You can modify the routing table if you want to specify which network to use.
Side Note: You should totally upgrade from XP to something newer if at all possible. Also, Pro and Home are mutually exclusive :)