In theory, yes, but there are a number of important factors to consider.
In general terms, the majority of funders willing to support capital projects for registered charities will be equally willing to support such projects run by Parish Councils, so charitable status doesn't open many doors to new funding sources. Funders will need to be satisfied that the applicant is sufficiently skilled and experienced to administer the grant, so a new charity would have to demonstrate that its individual trustees have that experience (unless the PC is the sole trustee), whereas a Parish Council that has operated successfully for up to 125 years provides greater reassurance to a funder. If a substantial portion of the funding is to be raised from donations from UK resident individuals, a charity could register for Gift Aid and claim the additional 25% from HMRC. However, apart from a few very minor concessions, charities have no exemption from VAT, whereas councils do.
Further down the line, if the charity has delivered the project, who will own the asset? Funders providing large grants will place onerous conditions on the applicant regarding future ownership and maintenance, so the charity would normally be prevented from gifting the asset to the council for a number of years.
I am aware of a number of projects that have blurred the lines and used a charity to raise the funds, but commissioned the works from the Parish Council and reclaimed the VAT. Local councils benefit from the lightest of touches in VAT regulation and inspection, but I believe that this is an abuse of the council's VAT concession that could result in action at a later date. Furthermore, unless the funders have given permission for the funds to be handed over to the council, this may represent a breach of the terms of the grant, which, in most cases, would require the grant to be returned.
This is a complicated scenario, but I hope I have provided some clarity, or at least highlighted issues for further consideration.