Reading https://github.com/ethereum/wiki/wiki/Light-client-protocol, it seems that it depends on the nature of the light client. If the client verifies any transactions, then that would increase security of the network. If it justs downloads them, then it seems that it would not increase the security of the network.
Of all four protocols on that page, the third protocol validates transactions, which would increase the security of the state, the second helps to ensure availability of transactions, the first helps to know the state of an accounts, and the fourth allows to watch event logs.
The purpose of the light client protocol is to allow users in low-capacity environments (embedded smart property environments, smartphones, browser extensions, some desktops, etc) to maintain a high-security assurance about the current state of some particular part of the Ethereum state or verify the execution of a transaction. Although full security is only possible for a full node, the light client protocol allows light nodes processing about 1KB of data per 2 minutes to receive data from the network about the parts of the state that are of concern to them, and be sure that the data is correct provided that the majority of miners are correctly following the protocol, and perhaps even only provided that at least one honest verifying full node exists.
So the security of light clients does rely on the assumption of an honest majority of miners (or perhaps that just one honest verifying full node exists).
