Foreign Direct Investment usually is founded on basically three objectives...tariff jumping motive; export development; rooting of inventions and innovations....if the motive for such investment is on the latter two objectives (exports development and innovation rooting), then there is a higher chance of FDI backing up National Innovation Capability. However, if the motive for such investment is for tariff jumping through trade implications, then there is relatively an insignificant room for FDI to play any role in National Innovation Capability. So in summary, the role of FDI in National Innovation Capability development depends on the motive/objective for such investment.
Innovations are wealth of a country because it returns heavily to the nation. At the same time it requires fund. FDI is one of the source. How the funding or collaboration links with the innovation regulation of a nation depends on country's policy.