Will a children's pullover rescale for an adult?
No, it almost certainly will not scale to fit you appropriately. But it could work with some reasonably simple adjustments. 

Explanation

In general, garments for babies and toddlers have shorter arms and shorter torso-length compared to the chest circumference than garments for adults. They sometimes also have a wider neck opening, and the size of the arm holes may be larger for ease of dressing and movement. 

If you scale a small child's pullover up to adult size based on the chest circumference, the arms and torso will be too short. But, if you can find out from the pattern the relevant dimensions of the finished garment, you can scale it all up, then work out how much extra length is needed. 

It would also be worth checking that the neck and arm hole sizes are appropriate, although if you are making a loose-fitting pullover, then these won't be as much of an issue. But different constructions will behave differently around the shoulders, as you expect. I expect that raglans and drop shoulders would be fine. I think round yokes are likely to be less easy. But the only way to really know is to do the maths!

Adding length

It would be easy to add length to the torso by adding some extra rows, although it may take some care to make sure you get whole repeats of any pattern(s).

Arms are likely to be tapered from the shoulder to the wrist. You should probably keep the same number of decreases, so you should add rows between decreases, to make the tapering appropriate for an adult.

Worked example

By comparing patterns for the same raglan pullover sized for adults:

https://www.purlsoho.com/create/2014/02/16/lauras-loop-the-purl-soho-friendly-fair-isle-sweater/

and children:

https://www.purlsoho.com/create/2015/01/02/friendly-fair-isle-sweater-now-sized-for-toddlers-kids-too/

(Note that I round to the nearest quarter inch and to the nearest 0.5 cm)

The adult size 40 has:


chest circumference of 40'' / 101.5 cm
total length 23'' / 58.5 cm 
arm length 18.5'' / 47 cm.


The child size (12 months) has


chest circumference 22.75'' / 58 cm
total length 12'' / 30.5 cm 
arm length 6.5'' / 16.5 cm.


If you scale the child size up to match the adults chest circumference, then you would have


gauge 7stitches x  9 rows per 4'' / 10 cm (very chunky!)
total length 21'' / 53cm (2'' / 5.5 cm / 4 rows shorter than adult)
arm length 11.5'' / 29 cm (7'' / 16 cm / 16 rows shorter)


So you can see that you would need to add 16 rows to the arms and 4 to the torso to match the adult size.

In your case, you could compare your scaled-up child's pattern to a different adult's pattern, or to a pullover that you own.