Does the presence of microvilli on a cell's surface ensure that it's more resistant to cell swelling or lysis in a hypotonic solution, as compared to a normal cell?
Microvilli, are cellular protrusions on the membrane and hence they increase the total surface area of the cell in context.
If we evaluate the characteristics of microvilli and the structural appearance, we know that; they have many small folds; strengthened and lined by the protein filament actin; bedded in a terminal web of alpha-actinin and keratin. All of these characteristics, work in harmony to support its ability, for it to do its function. That being, to allow greater diffusion whilst controlling the cells integrity. Evidently, the microvilli do help resist the hydrostatic pressure within a cell as a result to the distribution of pressure and the microfilaments present.
Most animal cells have microvilli so, there is a huge excess of factual evidence to support what happens to them in under specific conditions. Knowing this, it confuses me why you even asked this question. It just takes a simple comparison.
I'm presuming, a normal cell is a cuboidal cell, too. So, yes, if they were both placed in a variable hypotonic solutions, with gradual increases in concentrations for comparison, the cuboidal cell would rupture much earlier rather, the cell with the microvilli would be still standing at a further stage (concentration). However, the cell with the microvilli will nearly all of the time still lyse despite it's additions. Microvilli don't sorround the entire cell, if they did, the integrity of the cell in greater hypotonic solutions would be more applaudable vs a plant cell (cell wall containing pectin).
** http://www.histology.leeds.ac.uk/cell/cell_cytoskel.php ; 'keratin is a type intermediate filament in cells' [...] 'The nucleation of actin fibers occurs as a response to external stimuli, allowing a cell to alter its shape to suit a particular situation.'
** http://www.westfield.ma.edu/personalpages/draker/edcom/final/webprojects/sp10/cell/Ross44.jpg; 'A hypotonic solution has decreased solute concentration, and a net movement of water inside the cell, causing swelling or breakage.'
** http://www.histology.leeds.ac.uk/cell/cell_cytoskel.php ; 'Intermediate filaments are inserted into desmosomes at cell-cell junctions, and help to maintain cell-cell connectivity, as well as the structural integrity of the cell itself.'
P.s. Most of the answer was achieved by the application of knowledge so, direct references cannot be found!
Most animal cells have reservoirs of membrane, including microvilli (Sheetz et al, Annu. Rev. Biophys. Biomol. Struct. 2006. 35:417–34). This can help preventing lysis in hypotonic conditions, but has other functions as it allows the cell to take varied shapes without being constrained by its membrane area.
This is not volume regulation, by the way, but rather accomodation of volume changes. There is evidence that volume is regulated, but some osmotic challenges can be too great or to sudden for the volume response.