No. Inundate has negative connotations. Your friend's statement will ensure his rejection. Just say, "I am excited by research and feel very motivated to tackle more advanced problems." Don't try fancy writing. You or he can't manage it.

When I think of the word "inundate" I think of something like a flood, or a person with so much work to do that they can't handle it. It has a strong connotation with the word "overwhelm". You could try: “When I was doing my research, a sense of motivation to solve more difficult problems and the desire to delve into more advanced methods overcame me.” This is truer to the original meaning and style. I would, however, consider re-writing the sentence to make it less passive. This may be a cultural thing, but in the U.S., we’re taught to use the active voice when writing formally. The active voice tends to be easier to read and more interesting to the reader. So I would try something like: “When doing research, I found myself motivated to solve increasingly difficult problems and to delve into more advanced methods (of . ..). “ Or “The challenging nature of the research motivated me to solve increasingly difficult problems and to explore more advanced methods (of...).”