Would fundraising for an overseas volunteering trip count as a Voluntary Service section activity?

Yes and no. You cannot benefit directly from the money you fundraise. You can organize fundraisers that will be directly benefiting the project you are going to undertake, for example building materials and so on. You may not count fundraising as a Voluntary Service if the money is used to pay for your journey/programme, for example fees, flights, insurance, hotel accommodation and so on.