Let me start with an obligatory reference to one of the great worldbuilders of Science Fiction: Hal Clement.  In [Needle](https://en.wikipedia.org/wiki/Needle_%28novel%29) the alien visitor was a hard-SF take on the classic "blob".  It was explained that rather than being descendant from life using cells, it came from viruses, or something like that.

Note that researches work with "cell free" cultures, which is basically the gunk from inside a large number of cells but without walls cutting it up into little compartments.

Some "compartments" in nature are not microscopic.  Look at algae in particular.

> [![algae][1]][1]

> Valonia ventricosa, a species of algae with a diameter that ranges typically from 1 to 4 centimetres (0.39 to 1.57 in) is among the largest unicellular species

However, you asked about *complex*.

Eukaryote cells can have features like cilla and internal organelles by diving up the cell with more internal membranes.  A cell that's large in one dimension, like a muscle cell or nerve, can have multiple nuclei.

So what's the difference between a large cell and a bunch of cells?  Perhaps the distinction is less clear if the contents can move between them more easily and partitions can come and go.  But it will still be *like* multi-cells because it couldn't have a single nucleolus controlling everything.  It would still have a high degree of unit-ness even if boundaries are fluid.

[nigel222](http://worldbuilding.stackexchange.com/users/13883/nigel222) points out that a [plasmodial slime mold](https://en.wikipedia.org/wiki/Plasmodium_%28life_cycle%29) is exactly this: a single membrane without walls.  This supercell is known biologically as a [synctium](https://en.wikipedia.org/wiki/Syncytium) or [Coenocyte](https://en.wikipedia.org/wiki/Coenocyte) and is essentially a bag of cytoplasm containing thousands of nuclei.  Follow the links to those terms for more about your subject of interest here.

[![slime mold][2]][2]

You might look at The SETI weekly Colloquium on [Power laws, predictable evolution, and the limits of life](http://www.seti.org/weeky-lecture/power-laws-predictable-evolution-and-limits-life).  On one slide he shows that "things change" when limits are reached, and a higher level of organization is needed to make progress.  This includes the boundary between simple bag-like cells and those with complex internal organization, and again with the largest of those and multi-cellular life.  

So limits will need to be overcome at a particular size.  Could nature find a different way?  Multi-cellular life was an easy solution since cells divide anyway: just stick around and cooperate to greater degrees.  But understanding what the issues are with growing and maintaining itself with respect to energy and resources, you might find an idea to inspire a different solution that can be plausible in a good SF story.

Without cells arising at any point, you ask?  I don't think so.  What would keep all the *stuff* together, and how's that not a cell?  Maintaining a compartment to keep all the stuff together is thought to be an essential starting point for true life arising from protolife, but that could just be our limited imagination.  What do you even mean by not having cells at all?


  [1]: https://i.sstatic.net/Xh5Cd.jpg
  [2]: https://i.sstatic.net/O3XQF.jpg