How to prevent insertion of parskip glue?

You could do something like this

parindent=0ex
parskip=4cm

baselineskip=2cm

hbox tohsize{%
vtop{hsize=.3hsize
  hbox{aaa}
  hbox{bbb}
  hrule height 0mm depth 0mmrelax
  everypar{setbox0=lastboxendgrafeverypar{}vskip-2parskip}

  hbox{ccc} %<- TeX stays in restricted vertical mode
  parhbox tohsize{This is case 1hfill}

}hfillvrulehfill
vtop{hsize=.3hsize
  hbox{aaa}
  hbox{bbb}
  hrule height 0mm depth 0mmrelax
  everypar{setbox0=lastboxendgrafeverypar{}vskip-2parskip}

  ccc %<- TeX switches to horizontal mode
  parhbox tohsize{This is case 2hfill}
}%
}
bye

This answer is an attempt at further developing the answer of David Carlisle which aims at the hook everypar whose tokens are delivered whenever TeX due to switching to horizontal mode has just delivered vertical parskip-glue and started a horizontal list by inserting the hbox of width parindent.

As you focus on the "codes of the vtop" and not on the vtop itself I assume that the desired method is to work out also in (non-internal) vertical mode where probably some begingroup..endgroup-thingie might precede and more paragraphs might follow the hbox{ccc}/ccc/noindent ccc(?)-thingie.

Probably you can mess around with everypar, everyhbox, everyvbox, everymath, everydisplay to make sure that not only the next paragraph but generally the next thing that is typeset will cancel the changes to everyar. I have not yet thought about whether there are more obscure situations to consider in regard to "the next thing that is typeset".

In the example below the token skiprestore respective resetskiprestore is prepended permanently to each of the above-mentioned hooks. Usually these macros are no-ops.

The macro makemydamnverticalgap redefines

• resetskiprestore to redefine skiprestore and resetskiprestore as no-ops.
• skiprestore to apply the redefined resetskiprestore and to do some negative vertical skipping for cancelling out vertical parskip-glue, to do noindent in case the hbox inserted for starting the horizontal list had the width 0pt.

I decided for prepending tokens to the hooks permanently because then redefining these tokens can be done in terms of global which means that the desired changes will survive the wrapping into groups.

I don't know about the best way of implementing such a thing in LaTeX 2ε where the kernel itself plays around with all these every...-hooks.

Also in LaTeX there is, e.g., the package everyhook which allows you to mess around with the every...-hooks. Be aware that the current release (everyhook v1.2, dated 2014/11/26) has a bug which leads to amounts of consecutve hashes being halveed , e.g., ######## being halved to ####, whenever e.g., PushPreHook, PopPreHook, PushPostHook, PopPostHook and the like is carried out. (I addressed the issue on the package's GitHub-repository some months ago.)

parindent=3ex
parskip=.5cm

longdefexchange#1#2{#2#1}
longdeffirstoftwo#1#2{#1}
longdefsecondoftwo#1#2{#2}

newboxmybox

longgdefprependtohook#1#2{%
  #1=expandafter{romannumeral0expandafterexchangeexpandafter{the#1}{ #2}}
}%
prependtohookeverypar{skiprestore}
prependtohookeveryhbox{resetskiprestore}
prependtohookeveryvbox{resetskiprestore}
prependtohookeverymath{resetskiprestore}
prependtohookeverydisplay{resetskiprestore}
% I am not sure whether resetskiprestore should be done with other hooks also.

newboxmybox

gdefskiprestore{}%
gdefresetskiprestore{}%
longdefmakemydamnverticalgap#1{%
  endgraf
  hrule height 0mm depth 0mmrelaxnobreak
  kern#1nobreak
  hrule height 0mm depth 0mmrelax
  gdefresetskiprestore{gdefskiprestore{}gdefresetskiprestore{}}%
  gdefskiprestore{%
    resetskiprestore
    setboxmybox=lastbox
    vskip-2parskip
    endgrafifdimwdmybox>0pt elseexpandafternoindentfi
  }%
  ignorespaces
}%


noindent This is some paragraph.xleadershbox{This is some paragraph.}hfill This is some paragraph.
begingroup
makemydamnverticalgap{2cm}
endgroup
hbox{This does not switch to horizontal mode. There should be a vertical 2cm gap above this.}

This is another paragraph.

noindent This is some paragraph.xleadershbox{This is some paragraph.}hfill This is some paragraph.
begingroup
makemydamnverticalgap{2cm}
endgroup
leavevmode This does switch to horizontal mode. There should be a vertical 2cm gap above this.

This is another paragraph.

noindent This is some paragraph.xleadershbox{This is some paragraph.}hfill This is some paragraph.
begingroup
makemydamnverticalgap{2cm}
endgroup
noindent This does switch to horizontal mode. There should be a vertical 2cm gap above this.

This is another paragraph.

xleadersvbox{hrule height 0pt width 0ptpar This is another paragraph.}vfillbreak

parindent=1cm
parskip=4cm
baselineskip=2cm

hbox tohsize{%
  vtop{hsize=.25hsize
    hbox{aaa}
    hbox{bbb}
    makemydamnverticalgap{0cm}%

    hbox{ccc} %<- TeX stays in restricted vertical mo-de
    parvtop{noindent This is case 1 - TeX{} staying in restricted vertical mo-de}
  }hfillvrulehfill
  vtop{hsize=.25hsize
    hbox{aaa}
    hbox{bbb}
    makemydamnverticalgap{0cm}%

    ccc %<- TeX switches to horizontal mo-de
    parvtop{noindent This is case 2 - TeX{} switching to horizontal mo-de and inserting {ttstringpar-in-dent}}
  }hfillvrulehfill
  vtop{hsize=.25hsize
    hbox{aaa}
    hbox{bbb}
    makemydamnverticalgap{0cm}%

    noindent ccc %<- TeX switches to horizontal mo-de
    parvtop{noindent This is case 3 - TeX{} switching to horizontal mo-de and not inserting {ttstringpar-in-dent}}
  }
}

bye