I like this.
As said previously we currently don't know what causes matter to have mass and a gravitational attraction. If the LHC finds what we hope, the Higgs particle, we'll have an explanation for matter having a mass.
The higgs works (from my understanding anyway) in such a way that the more massive a particle the greater the interaction between it and the Higgs Field.
Now, I'll admit, when I was doing the course on this stuff, I wasn't the most interested...well, thats wrong, I was interested, but after writing a 4 line long equation that derived it...I sorta began to switch off.... I'm an experimentalist dammit
The way I understand the Higgs Boson and the Higgs Field is two fold,
Firstly the Higgs Field exists in all places in the universe and at all times, so it is similar to Space-Time in that respect.
The Higgs boson is the particle that couples matter to this field, the stronger the interaction with the Higgs boson the move massive a chunk of matter will be. Some matter interacts more strongly with the higgs than others, where as other stuff doesn't interact at all, ie photons.
Now, theory wise I can't remember there being any time component in any of the equations that describe the Higgs potential, however for a potential to act, time needs to pass.
So as Jon'C said, I think the distortions in Space-Time would still be there, the coupling of matter to the higgs field would still be there, but nothing would happen if time stopped, as with most things.
(oh, time may be a creation of man, but we might as well just use a measure of entropy to describe 'time". It would make life a crap load more difficult but entropy and time are really one and the same. As the universe gets old entropy increases and vice versa as entropy decreases so would time. Having a "standard", linear, analogous quantity to entropy just makes life easier.
This is all fine until we figure out a way to reverse entropy, currently thought to be impossible btw, but I think in Stargate and Star Trek they managed it somehow...maybe through an "Entropy Compensator" or something :P...yay for Sci-Fi)