Realistically, can a freelance writer place a fiction manuscript with today’s cautious publishers?

Yes. Fiction is the fastest-growing segment of publishing, including Christian publishing, especially in eBook formats. Fiction is our largest submission category. That does not mean it is easy for writers to get action from the publishers. A novel must have an intriguing plot, strong mechanics, and in a popular-selling fiction category to get attention.
A brief, 500-750 word synopsis of your fiction manuscript is a must, both for us to see as well as what a publisher will want to see. But describing fiction in a promotional way (and briefly) is very tough to do well. Helpful counsel on describing your novel can be found at www.honestediting.com, where you can receive help with your proposal for a fee.
Another option is a book from Writer’s Digest:  Give ‘Em What They Want by Blythe Camenson and Marshall Cook, subtitled The Right Way to Pitch Your Novel to Editors and Agents.