OfficialBubbleTanks

im afraid not, by a certain geometry theorem, if any two side lengths, when added, are not greater than the length of the third side, it is not a triangle. this eliminates many of the options. i shall cross out the eliminated ones

0,0

0,1

0,2

0,3

1,0

1,1

1,2

1,3

2,0

2,1

2,2

2,3

3,0

3,1

3,2

3,3

as you can see, there are 3/16 possible options left. i have taken geometry and have an entire binder of postulates and theorems. 

we have a 1/4 chance of each number for x and y, so there is a 1/16 chance for any given pair of numbers. 

a list of all possible pairs:

0,0

0,1

0,2

0,3

1,0

1,1

1,2

1,3

2,0

2,1

2,2

2,3

3,0

3,1

3,2

3,3

since 0 is an invalid number for a triangle, there is a 7/16 chance for an invalid triangle already. we continue to cross out invalids. also, if the sum of any two side lengths of a triangle is not greater than the length of the third side, it is an invalid triangle. 1,2 and 2,1 is invalid, so we have 9/16 invalid. 2,3 and 3,2 are invalid, 1,3 and 3,1 are invalid, now we have 13/16 invalid. 3,3 and 2,2 are isosceles so they are valid, and we already said 1,1 was valid. there is a 3/16 chance you would get a real triangle with side lengths 1, x, and y. this is an example with fair four sided dice. if it is done with unfair dice, the results could vary greatly.