If you have a slow network connection, your client will be bogged down by these requests. Because clients in the network are bogged down, searches often take a long time to return results. Results that trickle back a minute or two after the search are not uncommon. Just because no results have arrived doesn't mean results won't arrive in the future. Furthermore, Gnutella networks are created spontaneously and randomly.
Nothing prevents the networks from becoming segmented into disconnected parts.
If the client is connected via a modem, it simply will not be able to receive and process all of the search requests that come its way. Clients handle file downloading and serving, while servers handle processing search request. Thus, if a client has a slow network connection, it can still participate in the network by searching for, downloading, and serving files. If the client isn't serving very popular files and isn't downloading many files from others, very few connections will be established to it, and it will process very few messages. No search requests are ever processed by the client.