Yes:
$product = null;
$product->product_name = 'test';
$product->categories = array(2,6); // for the categories with the ids 2 and 6.
$price = null;
$price->price_value = 10;
$price->price_currency_id = 1;
$product->prices = array($price);
$productClass = hikashop_get('class.product');
$result = $productClass->save($product);
$productClass->updateCategories($product, $result);
$productClass->updatePrices($product, $result);
For a more complete example, you can look at the "saveForm" function of the product class which handle the saving of all the information of the product edition page.