Can I trust vector::size after an exception is thrown?

From the documentation for std::vector::push_back:

If an exception is thrown (which can be due to Allocator::allocate() or element copy/move constructor/assignment), this function has no effect (strong exception guarantee).

So in case of failure, the last push_back which caused the exception will be rolled back, but everything else will be fine: your vector will contain all of the previously pushed elements, and will be in a consistent state.

According to [vector.modifiers] (emphasis mine):

Remarks: Causes reallocation if the new size is greater than the old capacity. Reallocation invalidates all the references, pointers, and iterators referring to the elements in the sequence. If no reallocation happens, all the iterators and references before the insertion point remain valid. If an exception is thrown other than by the copy constructor, move constructor, assignment operator, or move assignment operator of T or by any InputIterator operation there are no effects. If an exception is thrown while inserting a single element at the end and T is CopyInsertable or is_­nothrow_­move_­constructible_­v<T> is true, there are no effects. Otherwise, if an exception is thrown by the move constructor of a non-CopyInsertable T, the effects are unspecified.

Since your T is int (and operations on integers never throw) you can only get the out-of-memory errors from std::vector when it attempts to allocate new memory for its contents, hence this function has no effect when throwing any exception and using size() afterwards is a perfectly valid approach.