I just ran some tests on some VPS services at Linode, Vultr and Digital Ocean. Running 4 CPU servers at each and running Tromp's solvers on rc2 using the 4 CPUs package at each I got the following: Vultr: 3.83 Sol/s, Linode: 3.14 Sol/s, Digital Ocean: 3.17 (each completed a minimum of 10,000 Equihash solver runs).
These servers cost $40, $40 and $80 a month respectively. Taking the best case of Vultr $40 a month for 3.83 Sol/s that's 0.1925 BTC per year for 1 H/s whereas cloud mining is currently cheaper (e.g. Zeropond at 0.156 BTC and GM cheaper at 0.0742 BTC albeit sold out). There will be optimizations to the miner but I imagine that will apply to both the native miner as well as the cloud offerings so long story short if you are thinking of mining on one of these cheap VPS providers it is likely not worth it (I believe it also may violate their T&C for excessive CPU use).
EC2 benchmarks would be interesting particularly GPU instances using Zogminer https://forum.z.cash/t/zogminer-open-source-gpu-miner/2152/237