Yes it does matter for "some".. Carrier oils release at different rates, thus this will effect the serum levels of the parenting hormone, however the carrier really has little effect on a scale that you or anyone would even notice aside from its " kinetic profile under clinical investigation/studies" , although administration with certain carriers may yield different toxicological profiles for the same drug, some reaching supraphysiological serum testosterone levels, but this will vary with administered route (whether IM or subQ), different esters, individuals and so on..Also, different regions favor one oil over the other like western pharmacopoeia practice may often and commonly use Grape-seed, as in other regions of the world with therapies some use tea-seed oil,soy and cottonseed with the same promising returns (pro's and con's with both oils), much like Enanthate is manufactured in Europe for TRT, while Cypionate is manufactured in the U.S. Testosterone Cypionate and Enanthate both steroids have the same effects and functions, whilst there are studies claiming the longevity effect of Cypionate compared to Enanthate differ,but we know it's irrelevant on the small scale..The same can be seen and recognized with carriers to a degree, this is why most UGL's will use the same carriers to keep release time with-in a narrow range of others..

Now if we're talking about supraphysiological serum testosterone levels, with shorter esters in different carrier oils that possess different half-life/molecule weight (yes carrier half life's), with different routes of administration sub-q or IM? Sure, we can see levels exceeding upper limits, but the extended release will balance out with a decline (ester dependent), this is just a quesstimation as there will be many variables to conciser (age,genetics) but you get the jist on the generalization here.

In the grand scheme of it all, It comes down to 90% allergies and user sensitivity..

Site reaction, immune response and even hormone release will have effects on each independent user..(Example - castor oil has a slow, stable, steady release for heavier esters due to its longer half-life)..
However for most generally used carriers the viscosity really isn't that different when compared through kinematic viscosity measurement (mm2/s) - Fluid resistance..

When being measured they're off by a few digits, but that's so insignificant..It's mainly immune response/allergies/site irritation..

Below is a "basic" template of kinematic viscosity measurements (mm2/s) - Fluid resistance with most major carrier oils. Top being thickest, and last being thinnest..

Castor 297.0
Crambe 53.6
High-Oleic Safflower 41.2
Peanut 39.6
Sunflower 37.1
Grapeseed 37.0
Sesame 35.3
Corn 34.9
Cottonseed 33.5
Soybean 32.6
Safflower 31.3

Here is a study explaining how "castor oi" has a longer half-life than most traditionally used carriers in general practice

Intramuscular injection of testosterone undecanoate for the treatment of male hypogonadism: phase I studies.

Behre HM1, Abshagen K, Oettel M, Hübler D, Nieschlag E.
Author information

Abstract

OBJECTIVE:

In the search for long-acting testosterone preparations suited for substitution therapy of hypogonadal men, testosterone undecanoate (TU) dissolved in either tea seed oil or castor oil was investigated.
DESIGN:

In study I, 1000 mg TU in tea seed oil (125 mg/ml) were injected in equal parts into the gluteal muscles of seven hypogonadal men. In study II, 1000 mg TU in castor oil (250 mg/ml) were injected into one gluteal muscle of 14 patients.
RESULTS:

In comparison with published data on testosterone enanthate, most widely used for i.m. injections, the kinetic profiles of both TU preparations showed extended half-lives and serum levels not exceeding the upper limit of normal. The castor oil preparation had a longer half-life than TU in tea seed oil (33.9+/-4.9 vs 20.9+/-6.0 days (mean pm S.E.M.)).
CONCLUSION:

The longer half-life and the smaller injection volume make TU in castor oil a strong candidate for further applications in substitution therapy and in trials for male contraception.

Abstract
In the search for long-acting testosterone preparations suited for substitution therapy of hypogonadal men, testosterone undecanoate (TU) dissolved in either tea seed oil or castor oil was investigated.In study I, 1000 mg TU in tea seed oil (125 mg/ml) were injected in equal parts into the gluteal muscles of seven hypogonadal men. In study II, 1000 mg TU in castor oil (250 mg/ml) were injected into one gluteal muscle of 14 patients.In comparison with published data on testosterone enanthate, most widely used for i.m. injections, the kinetic profiles of both TU preparations showed extended half-lives and serum levels not exceeding the upper limit of normal. The castor oil preparation had a longer half-life than TU in tea seed oil (33.9+/-4.9 vs 20.9+/-6.0 days (mean pm S.E.M.)).The longer half-life and the smaller injection volume make TU in castor oil a strong candidate for further applications in substitution therapy and in trials for male contraception.


Below is a great read about treatments, and serum levels with carrier oils!
Intramuscular injection of testosterone undecanoate for the treatment of male hypogonadism: Phase I studies