I don't see anything wrong in grammar but it does seem unnatural. First, it's not exact that '和' can't be used to connect verbs. '和' can not be used to connect predicates. For example, we don't say 我看书和听歌. But in '我去中国旅游和学习(I will go to China for travel and study)', ‘旅游’ and '学习' are used as object after the invisible 'for', '去' is the predicate in the sentence. So, it's OK to use '和'. There are many ways to connect verbs. I can't explain clearly why '也' is not porper in the sentence because it does sound better if you use ‘学习汉语’ instead of ‘学习’......One reason is that this sub-clause is too short to be the end of the whole sentence.