Will TiVo stream YouTube better with a better percentage signal strength?

Will TiVo stream YouTube better with a better percentage signal
strength?

We set up our new TiVo HD-XL in a room that's a couple thick-walled
rooms away from our wireless router.  The TiVo re****ts its network
signal strength as "Marginal," giving numbers between 35% and 49%
(while our older TiVo, in the same room as the router, re****ts
"Excellent" at 80%).

We watched a few YouTube videos last night on the new ("Marginal"
signal) TiVo.  They were kind of low-res, having problems when the
video had a lot of motion, as you'd expect from YouTube videos.  

I'm wondering:
Would the videos display better if we could increase the signal's
percentage?  Would doubling the signal's percentage -- say, from 40%
to 80%, also double the "throughput," or transfer rate, or kbps?  (Or,
if not doubling it, increase it by a very noticeable amount?)

I think that YouTube is now "smart" about offering higher quality
video when it can see that a user has a faster connection.  If so, and
if the answer to the first question is yes, would YouTube videos then
look better on our new TiVo?

(I'm not sure exactly how I'd double the signal percentage on our
LinkSys router -- presumably either by attaching a signal booster
directly to it or by sticking another router/booster/extender/whatever
halfway between our current router and the new TiVo's wireless
receiver.  But I wouldn't ever bother with that step unless I believed
that increasing the signal from 40% would actually get me something I
needed.)


Thanks in advance for any input.