If a share split occurs, it means that the share price was considered too high. It produces more flexibility in trading volumes, and stability to the share price. Generally its an indicator that the company is performing well. I found out share mergers occur also in the game meaning, which is basically the opposite.
You can probably get away with IPOing after the share split, as there will probably be increased investor interest. But IPOing before a share split may prevent a share split from happening, the result on shares will be the same but the assets will go into the corporation not the shareholders (you), also it will cause a decrease of share ownership for all existing shareholders to facilitate these new shares. Its up to you. Creating new shares (IPO) gives you a smaller slice of the companies asset growth (your asset growth) unless you buy back all the shares just IPOed (which is basically you pumping cash into a public corp), share splits pass the expected asset growth fully onto the shareholders. Creating new shares through IPO (except the first IPO) aren't really a good idea unless the corporations is a bit low on cash.