I believe that foreign aid is a good way to promote internationalism as long as the country receiving the aid wants it. I do not think it is a good thing to force it-this makes it look as if there is a hidden agenda. I also think that foreign aid is great as long as it is within the financial means of the country supplying the aid.
I would say that this is as good a way as any to promote internationalism. As the previous post says, any cooperation between two countries is going to promote internationalism, so the question is whether aid is a good way to go about doing that. I think that if aid is done properly, it will promote internationalism. However, if it is done wrong it might make the recipient country feel pushed around (if there are too many conditions on the aid) or it might make the donors feel like suckers (if there are no conditions).
Though the term foreign aid seems to imply that one country is giving some thing free to another nation without getting or expecting any other goods in return. However, barring some instances like help given at the time of natural disasters, the foreign aid is rarely such altruistic activity. Whatever aid the donor nation gives, is given with strings attached that ensure that the donor nation more than compensated for the cost incurred by it in one way or the other. Similarly the nation receiving aid also accepts it and the string attached in the expectation that the benefit of the entire deal is more than the costs. Thus both the countries hope to benefit from the deal. To what extent the two countries actually benefit is dependent on the nature of deal.
In general any cooperation between two countries promotes internationalism, and foreign aid is a form of cooperation. In this way it definitely promotes internationalism. However, I do not see any point in promoting internationalism itself through foreign aid or any other means. Internationalism is one of he many routes to improving common welfare of nations practicing it. But it is a means to to achieve the objectives of common welfare. It is not an objective that needs to be pursued in isolation.